McAvennie eventually found his form at Parkhead, and his 15 goals in 1987–88 helped Celtic to a Scottish Premier Division and Scottish Cup double. That season (the club's centenary season), he was part of a formidable front trio for Celtic comprising himself, Andy Walker and Joe Miller. One of the high-points during the season for McAvennie were his two goals in Celtic's 2–0 win over Rangers in January 1988. The Cup Final in May was particularly memorable for McAvennie as he scored two late goals to beat Dundee United 2–1, the winning goal coming in the final minute.