Everton's Premier League campaign began in August 2013 with Martínez changing their style of play to a possession based, attractive brand of football which initially led to three successive draws to start the season. A first victory came in the next match 1–0 against Chelsea and by Christmas Everton had only suffered one defeat, a run which included a win over Moyes' Manchester United, the first time the club had tasted success at Old Trafford in 21 years. The team almost went an entire year unbeaten at home but lost 1–0 against Sunderland on Boxing Day. Everton's progress stalled somewhat in the early part of 2014 with three losses in four games against Liverpool, Tottenham Hotspur and Chelsea, before winning seven league games in a row for the first time since 1987. The spell contained perhaps Everton's best performance of the season when they defeated Arsenal 3–0. The streak was ended with a 3–2 home defeat by Crystal Palace, but Everton returned to do the double over Manchester United for the first time since 1969. Moyes was sacked as their manager a day later. Two defeats in a row after this ended Everton's Champions League hopes but a finish of 5th in the league table is their highest in five years with Everton qualifying for next season's Europa League. Martínez utilised the loan market during the season, with Romelu Lukaku (on loan from Chelsea) being Everton's top scorer with 16 goals in all competitions. The emergence of young players such as Ross Barkley, John Stones and summer signing James McCarthy was also a feature of his debut season in charge, with Barkley going on to be selected for England's World Cup squad. Right back Séamus Coleman was named Everton's player of the year.
In the cup competitions Everton lost in the sixth round of the FA Cup (entered at round three) and the third round of the League Cup (entered at round two).
Everton announced on 25 May 2013 that the club would be competing in the inaugural edition of the International Champions Cup, based in venues across the United States and in one European city, and held between 27 July and 7 August 2013. The opening fixtures were announced four days later, with Everton playing 2012–13 Serie A champions Juventus in the first round.
Arouna Koné, a 29-year-old Ivorian striker who scored 11 goals in his debut Premier League campaign in the previous season. Everton met a £5 million release clause and beat off the competition of Newcastle United to sign him.
Antolín Alcaraz, a 30-year-old Paraguayan central defender who joined on a free transfer after his contract at Wigan had expired. He had been at Wigan for three seasons but saw his 2012–13 season curtailed due to a groin injury.
Joel Robles, a 23-year-old Spanish goalkeeper who had spent last year on loan to Wigan from Atlético Madrid. He joined on a five-year contract for an undisclosed fee.
Everton also signed 19-year-old Spanish forward Gerard Deulofeu on a season-long loan from Barcelona the following day, on 10 July 2013.
Victor Anichebe was transferred to West Bromwich Albion in a deal which could rise to £6 million. The striker had made 168 appearances for the club, scoring 26 goals.
Everton's first league win of the season came with a 1–0 home success over Chelsea with Steven Naismith getting the game's only goal. They then came back from 2–1 down to beat West Ham United 3–2 at Upton Park as Leighton Baines scored two free-kicks and Romelu Lukaku became the first Everton player since Alan Ball in 1966 to score a winner on their debut. The result also made Roberto Martínez the first ever manager in the club's history to be unbeaten in their first six games. However, the run did not last as in the next fixture Fulham won 2–1 in the third round of the League Cup. New striker Lukaku continued his early form for the club by scoring two goals in the next league game against Newcastle United in a match where Everton led 3–0 at half-time and survived a second half comeback to win 3–2.
Everton's unbeaten run in the Premier League at the start of the season came to an end on 5 October when it was defeated by Manchester City by 3–1 at the City of Manchester Stadium. After the international break the following week, Everton returned to winning ways with a 2–1 home victory over Hull City, which saw Steven Pienaar score the winning goal just 10 seconds after coming off the bench, making his return to the side from a hamstring injury. A 2–0 away win over Aston Villa the following week saw Romelu Lukaku score his fifth goal in as many league appearances for Everton, and momentarily moved the club into fourth position on the league table.
Everton began the month with a 0–0 home draw against Tottenham Hotspur which meant the club had only suffered one defeat from their opening 10 games in successive seasons for the first time in its history. Another 0–0 draw followed before the first Merseyside derby of the season during which Everton came from 2–1 down to lead 3–2, before an 89th minute Liverpool goal saw the game end 3–3. Everton returned to winning ways by defeating Stoke City 4–0 with both Gerard Deulofeu and Bryan Oviedo scoring their first league goals for the club. Romelu Lukaku continued his impressive start to the season by scoring his eighth goal in ten games as Everton finished the month in the Champions League places. With Oviedo and Séamus Coleman both scoring it was the first time in Everton's history that both fullbacks found the net during a game.
The next fixture saw Manchester United manager David Moyes face his former club for the first time and it was Everton who won 1–0 to record their first victory at Old Trafford for the first time in 21 years with another goal from Oviedo. Deulofeu scored an 84th-minute goal to earn a 1–1 draw with league leaders Arsenal at the Emirates Stadium in the next fixture. Everton then beat Fulham at home for the 21st consecutive time with a 4–1 win as Leon Osman scored on his 300th league appearance for the club. Everton then travelled to Swansea and won 2–1, maintaining their record of never having lost to the Welsh side in any fixture. The club then suffered a setback to bottom of the table Sunderland, losing at home in the league for the first time in a year, after Tim Howard conceded an early penalty and was sent off in the 25th minute. Winning ways were restored in the following fixture against Southampton with goals from Coleman and Lukaku, his first in five league starts, to ensure Everton ended 2013 fourth in the table.
Nikica Jelavić's two-year stay at the club ended after he moved to Hull City. The striker had enjoyed a fast start for Everton by scoring nine goals in his first thirteen games, but netted just two goals in the whole of 2013. He had fallen behind Romelu Lukaku as the first choice striker and also moved in a bid to improve his chances of selection in Croatia's squad for the World Cup.
John Heitinga moved to Fulham after four and a half years at Everton. He had struggled for first team football during the season having failed to start a single league game, but did score on his final appearance for the club in an FA Cup fixture against Stevenage.
Kevin Mirallas scored a fantastic 25 yard freekick as Everton came from a goal down to beat Aston Villa 2–1. Everton lost for the second time in three games as Tottenham Hotspur defeated them 1–0 at White Hart Lane, but their form in the FA Cup continued with a 3–1 home success over Swansea City to reach the quarter-finals. The club then lost a second league game in a row for the first time this season when Chelsea scored a stoppage time winner at Stamford Bridge.
Romelu Lukaku returned from an ankle injury to score a late goal in a 1–0 win over West Ham United to begin March, but Everton were knocked out of the FA Cup following a 4–1 defeat to Arsenal which means the club have now failed to beat the Gunners in the last 20 away meetings.Séamus Coleman's miscued shot in the last minute of the next game against Cardiff City ensured Everton responded with a 2–1 victory to be placed sixth in the table. The club then won four league games in a row for the first time in six years by defeating Newcastle United 3–0 thanks to an amazing solo goal from Ross Barkley who dribbled from inside his own half to score the opener. It was Everton's biggest win at Newcastle in 47 years. Everton ended the month with a fifth successive victory for the first time since 2002 with a 3–1 away win over Fulham.
Everton beat Champions League rivals Arsenal 3–0 at home in a performance manager Martínez described as tactically perfect. The result left the side a point behind the fourth placed Gunners with a game in hand. A seventh successive league win for the first time since 1987 followed with a 1–0 victory over Sunderland which moved the club into fourth place. It also took them to 65 points, the highest total Everton have ever amassed in a Premier League season. The club then handed the initiative back to Arsenal in the race for Champions League football as they lost 3–2 at home to Crystal Palace. Everton responded with a 2–0 victory over Manchester United and in doing so did the double over for the reigning champions for the first time since 1969. Everton's previous manager David Moyes was sacked by United a day later after just 10 months in charge. However, Everton then lost 2–0 against Southampton (with own goals from Antolín Alcaraz and Séamus Coleman) and 3–2 to Manchester City to end their chances of finishing the campaign in fourth place. Before the Manchester City game there had been rumours that Everton would not try 100% or field a weakened side as any positive result would give rivals Liverpool the impetus in the race for the title. Roberto Martínez insisted his team would be giving everything they had for the win and, despite the loss, he said afterwards that he was proud of the effort of the players. Everton finished the season by winning 2–0 away at FA Cup finalists Hull City to finish fifth in the table and qualify for next season's Europa League.
"Attendances have been fantastic this season. If you look at the past four or five seasons and look at the number of full houses and look at average attendances, then the trend has been very positive. In 2013/14, we've had nine full houses and we're very pleased and very proud to have had that. We've also had an average attendance of well over 37,500, and I think as everybody knows, when we get to 36,000 at Goodison we start selling restricted view seats. To be substantially ahead of that figure is a great achievement. What it means is we've now set a very ambitious target for next season. That target is that three out of every four seats will be pre-sold before the first ball of the season is kicked. When you add in hospitality sales and the Season Ticket target, we're looking at 30,000 tickets already pre-sold, and that would be really great news for the football club."