Stevens began his career with Bolton Wanderers and established himself in the side as a scheming inside-forward, winning the FA Cup in 1958. He joined Everton in 1962 as cover, shortly before Bobby Collins moved to Leeds United. He became a vital member of Everton's midfield, being an ever-present in the League over two seasons and winning a League Championship medal in 1963, quickly followed by winning the 1963 FA Charity Shield. After leaving Everton, he played for Oldham Athletic and Tranmere Rovers.