Kris Commons scored from the spot in the 18th minute after Gorgie midfielder Jamie Hamill was controversially penalised for handball before Jason Holt equalised in the 56th with a deflected drive from the edge of the box.
Anthony Stokes put Celtic back in front after 65 minutes with an unstoppable volley from 12 yards before substitute Pukki, who replaced Commons, made it 3-1 five minutes from time to make a perfect start to his Hoops career following his move from Schalke 04.
It was a good work-out for the champions ahead of their opening Champions League fixture against AC Milan in the San Siro on Wednesday night.
Hearts remain bottom of the table on minus eight points as they try to recover from the 15-point penalty for lapsing into administration but boss Gary Locke can be happy with the effort from his players.
Finland international Pukki could only find a place on the Hoops bench as Neil Lennon kept an unchanged side from the one that won at Dundee United.
Jambos' skipper Danny Wilson and defender Kevin McHattie both returned from league suspension.
It was a youthful Hearts side which struggled to cope with Celtic's confident start to the game.
However, in the fifth minute, after Hoops left-back Emilio Izaguirre was penalised by referee Willie Collum for handball 25 yards from goal, Fraser Forster had to dive to his right to beat away McHattie's free-kick which was sneaking in at the far post.
The visitors still looked in control and came close in the 13th minute when Derk Boerrigter's cross on the run from the left was volleyed over the bar by Commons.