Evans was born in Didcot (now in Oxfordshire, but then in Berkshire) in 1936. He signed for Reading in 1952 as a ground staff junior, aged just 16. He soon won his place at left-half in the first team and held it throughout the adversities of National Service in the RAF. He went on to make the wing-half position his own for the next ten seasons, and was a skilful, thoughtful player without an ounce of malice in him, playing 459 first-team games without being booked once. He was selected as reserve for the Third Division South side against the North in April 1957 and also October 1957. In a vote to compile the Royals' best-ever eleven, Evans was voted the best right-winger with 48.4% of the vote .
After leaving the club in 1967, he briefly took over as player-manager at Andover before joining Shrewsbury as player-coach, eventually becoming their manager in 1972. He returned to Elm Park as Charlie Hurley's assistant manager in 1974, and finally took over as manager in 1977. He managed the 1978–79 championship-winning team, securing the Manager Of The Year Award in the process. He remained Reading manager until 1984, making perceptive signings from non-league football such as Kerry Dixon and Trevor Senior. Dixon was later capped several times by England and for almost a decade was Chelsea's top goalscorer. Senior never achieved the heights experienced by Dixon, although he was a highly accomplished goalscorer for Reading, particularly when they won promotion to the Second Division as Third Division champions in 1985–86.
Evans then joined Oxford United as Chief Scout and Youth Development Officer. He became the manager after the resignation of Jim Smith in the summer of 1985, and led the team in their first season in the top flight of English football. The season ended with United beating QPR (managed by Smith) 3–0 in the final of the Milk Cup at Wembley, and avoiding relegation by achieving the same scoreline over Arsenal in the last game of the season a week or so later. At the Wembley final, Evans famously sent up long-serving club physio Ken Fish in his place to collect his winner's medal, a gesture seen as typifying his modesty and generosity.
In November 1986 Oxford briefly occupied eighth place in the First Division — their highest standing to date — but they finished 18th in the final table and Evans resigned in March 1988 just before Oxford's relegation. He continued at the club in various capacities, including a brief stint as caretaker manager in 1993 and elevation to the board of directors in 1998, before rejoining Reading as Chief Scout in November 1999.
He died of a heart attack on 18 August 2000 at the age of 63. A plaque was placed in the wall of the Madejski Stadium by Reading F.C. in his memory, reading "Maurice Evans, 1936–2000. Player, Manager, Gentleman". A lounge at the Kassam Stadium is also named in his honour.