On 17 July 2009, Palacio signed a four-year contract with Genoa in the Italian Serie A for €2.81 million to replace Inter Milan-bound Diego Milito and help out his fellow Argentine Hernán Crespo at forward. Alongside Crespo, Palacio had joined another Argentine, Luciano Figueroa, who had been on loan with him at Boca Juniors throughout 2008. During his first few months, Palacio would miss out on two matches after suffering a small ankle injury. On 5 November, Palacio scored his first goal with Genoa in a 3–2 victory over Lille OSC in the 2009–10 UEFA Europa League competition.
On 22 May 2012, Genoa President Enrico Preziosi confirmed that Palacio would become an Internazionale player for the 2012–13 season. On 7 June, he was officially sold to Inter for €10.5 million, signing a three-year contract paying the player €2.7 million per annum.
Palacio debuted in a UEFA Europa League qualification match against Croatian side Hajduk Split. Palacio scored his first Inter double in a friendly against CA Bizertin of Tunisia on 18 August. He then scored his first official goal for Inter on 23 August in the play-off round of Europa League qualifiers against Romania's FC Vaslui. He scored again in the return leg in Milan on 30 August, making the match 1–1 as Inter progressed.
He scored his first goal in Serie A for Inter on 21 October in a 2–0 victory at the San Siro against Catania. On 4 November, he scored the final goal in a 1–3 win against defending league champions Juventus while on 8 November, he scored a brace in a Europa League match against FK Partizan (1–3) that advanced Inter into the competition's Round of 16 with two Group Stage matches to spare. During a second round match in the Coppa Italia against Verona on 18 December, after the injury to goalkeeper Luca Castellazzi and after all three of the club's substitutions were exhausted, Palacio, wearing Vid Belec's jersey number 27, was put into the goal for the final 15 minutes of the match. He failed to concede a goal to the opposition in a 2–0 final win and even made a fine save in the 91st minute, stopping a diving header from the right side of goal by Verona midfielder Alessandro Carrozza. .
On 14 February 2013, in a match against Romanian side CFR Cluj in the first leg of the Europa League Round of 16, Palacio was substituted seven minutes into the game after a season-ending injury to starter Diego Milito. Palacio came on and finished the game with both goals scored in a 2–0 victory. On 3 March, against Catania, Palacio was substituted on at the beginning of the second half at a time when the Nerazzurri were down 2–0. Palacio went on to provide assist for Ricky Álvarez's goal, then scored twice himself, leading Inter to a 2–3 comeback victory. On 3 April, Palacio scored his second double of the league season against Sampdoria, raising his tally to 12 goals scored; in the same game, however, he strained his left hamstring, ultimately ending his season prematurely.
Palacio started the game against Genoa on 25 August and finished off Genoa with a goal in stoppage time, giving Inter a 2–0 lead. On 14 March 2014, Palacio signed a new two-and-a-half year contract with the I Nerazzurri side, which will keep him at the club until 2016.