Stevenson had been ousted out of Rangers by the signing of legend Jim Baxter and spent a few months in Australia, but didn't get a clearence to play down under. When he returned to Glasgow Shankly outbid Preston for his services. He was a skillful performer, playing on the left-side of midfield. Stevenson was the dressing room joker and a big favourite with the fans. Stevenson arrived on Merseyside in October 1962 and took over the left-half spot from Tommy Leishman. Liverpool consolidated their First Division status after 8 years away by finishing 8th and then, with one of the most-settled sides in the club's history, took the championship itself a year later. Stevenson missed just 4 league fixtures in the 1964-64 season and only 3 the following season, when disappointment at failing to successfully defend their title was amply compensated for on the 1st of May 1965 when, after a wait of over 70 years, the FA cup finally made its way into Liverpool's trophy cabinet for the first time. Willie won a second championship medal in 1966 and was also a regular member of the side in the first few exciting years of European club competition but when the 1967-68 season opened it was Emlyn Hughes who was wearing the No. 6 shirt. Stevenson was only picked once more for the first-team, a home fixture with Wolves on 25th November 1967 in which he scored with a late and decisive penalty-kick. Still only 28 years old, he was far too good a player to be languishing in a reserve-team and it came as no surprise when he decided to accept Stoke City's offer in December 1967. Stevenson made 82 league appearances for Stoke before returning to Merseyside with Tranmere.