During the war, while continuing to play for Everton, Stevenson also enlisted in the RAF. Between 1939 and 1946 he made 202 appearances and scored 89 goals for Everton in wartime regional leagues. One of the highlights of his wartime career came on 1 June 1940 when he scored a hat-trick in the last five minutes of a game against Manchester United. As well as playing for Everton, he also turned out as a guest for both Tranmere Rovers and Blackpool. After the war Stevenson played in an Everton team that also included fellow Irish internationals Peter Farrell, Tommy Eglington and Peter Corr and future team manager Harry Catterick. By the time he finished his career with the club he had made 255 English League appearances and scored 82 league goals. He also played a further 16 games and scored a further 8 goals in the FA Cup. He made his final league appearance for Everton on 7 May 1949.
