Coventry City 3 Celtic 1
A crowd of 25,075 were treated to an action-packed encounter which featured first-half goals from City's Dennis Wise and the Bhoys' Shunsuke Nakamura before Sky Blues substitutes Kevin Thornton and Liam Davis struck after the interval.
The 37-year-old Shaw, now enjoying his tenth full season with the Sky Blues, started the game in his accustomed central defensive position against a Celtic side managed by Gordon Strachan on his first return to Coventry since his exit as City boss in 2001.
Wise was first to score in only the second minute after referee Dermot Gallagher awarded the hosts a free-kick 20 yards from the Celtic goal following a foul on Stern John. The 39-year-old Wise stepped up to sweep home a low, curling effort past goalkeeper David Marshall.
The Scottish champions equalised in the sixth minute when Nakamura hit a low, 20-yard shot past Morten Fulop.
Both sides made changes at the start of the second half. Stuart Giddings returned to the Coventry side after recovering from two knee operations. Former Coventry striker Dion Dublin was one of three Hoops substitutions.
Just past the hour Don Hutchison set free Thornton who burst into the Celtic box, pulled the ball over a diving Marshall and then stylishly turned to dump Stephen McManus on his backside before hammering the ball home. Davis then wrapped things up with a cute finish with 78 minutes gone.