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.
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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.
Celtic got the breakthrough when Collum pointed to the spot after adjudging Hamill to have handled as he challenged Stokes following a corner by Commons.
The former Kilmarnock player, who was only available after successfully appealing the red card he picked up against Inverness for deliberate hand ball in conceding a penalty before the international break, was shocked.
It did not look as if he could have got out of the way of the ball but after receiving a yellow card, his frustration was compounded when the former Nottingham Forest player drove the penalty past Jamie MacDonald.
The champions took a tighter grip on proceedings as the home fans turned on Collum.
Stokes had the ball in the Jambos net in the 27th minute when he followed up on a Commons cross but was ruled offside.
However, that disappointment served only to cajole Lennon's side into stepping up their efforts.
In the 34th minute a powerful drive from Celtic midfielder Adam Matthews had MacDonald scrambling low to his left to make a good save with Jamie Walker completing the clearance.
Just before the break, a great saving tackle inside the Hearts box by McHattie on Matthews, which led to the Wales international being replaced by forward Georgios Samaras with a Celtic reshuffle ensuing, prevented the visitors almost certainly doubling their lead.
There was a more insipid start to the second-half and there was an element of fortune with Hearts' leveller.
McHattie's shot from outside the box was cleared only to Holt whose drive took a deflection before nestling behind Forster, whose attempted save with his foot was futile.
Samaras turned a Stokes cross over the bar from close range within seconds of the restart and the goal seemed to shake Celtic out of their slumber.
And when Commons sent Stokes through with a clever header, the Irishman took a good touch before thrashing the ball past MacDonald from 12 yards, before picking up a booking for his celebrations.
As Celtic turned the screw, MacDonald made a good save from an Izaguirre drive before Samaras missed another good chance in the 72nd minute, knocking Boerrigter's cross wide of the target from a couple of yards out.
In between, Pukki replaced Commons and when he was set up brilliantly by Stokes with five minutes remaining he could do little more than head into the corner of the net to seal the win.