Viollet joined Manchester United on 1 September 1949. He came through the junior ranks at United and turned professional in 1950. His first game for the club came against arch-rivals Newcastle United on 11 April 1953. He was a striker, along with Tommy Taylor for the Busby Babes of the 1950s. He was a survivor of the Munich air disaster. Viollet played a key role in the championship-winning teams of 1956 and 1957, which paved the way for United's first two campaigns in the European Cup, where they reached the semi-finals both times.