Connolly was born in Barrhead, Scotland and began his football career as a junior with Glasgow United before turning professional with St Johnstone in January 1968. Connolly played in the 1969 Scottish League Cup Final at Hampden Park versus Celtic, who were on their way to their second European Cup Final in four seasons. The Perth club lost narrowly 1–0 with Connolly later commenting, "We gave them the fright of their lives". The Perth Saints plundered league wins at Ibrox Park and Celtic Park with Connolly in their ranks.