The Hoops suffered a record 6-1 defeat away to Barcelona in midweek that capped off a disappointing UEFA Champions League campaign.
It has been a different story domestically, however, with the Hoops now sitting seven points clear at the top of the Scottish Premiership and are still unbeaten on league duty.
Celtic looked comfortable in the first half as they stroked the ball about the park at ease, with their biggest challenge coming from the heavy rain and high winds that battered Celtic Park throughout the match.
However, their lack of a killer touch in front of goal meant they failed to find an opener until the 29th minute when the much-maligned Pukki tapped home from close range after good work from the Hoops.
Hibs improved in the second half as Celtic's European exertions began to take their toll and came close to an equaliser on the hour mark when Liam Craig hit the post with a shot in the box.
Substitute Abdellah Zoubir saw his strike held by Fraser Forster and Craig sent a late header just wide as Terry Butcher suffered his first defeat in charge of Hibs since joining the club late last month.
"Hibs set their stall out from the first minute to make it difficult to break them down and we were forced to do all the running," Celtic manager Neil Lennon said.
"Fatigue kicked-in in the second half and we could see a lot of heavy legs out there and naturally so after a big game in midweek."
His Hibernian counterpart said his side could take confidence from their performance against a Celtic side that had scored 12 in their past two domestic matches.
"Our game plan in the first half was to frustrate them and the crowd and it worked for about 28 minutes when we gave the ball away and they capitalised on it and scored," Butcher said.
"I was really pleased with the way we played and our effort and commitment. Celtic were putting the ball into the corner at the end to hold on to a 1-0 win which shows you just how far we have come."
Lennon had made three changes to the side that were humiliated in Barcelona with Kris Commons and Anthony Stokes restored to the side with Derk Boerrigter and Georgios Samaras dropping out.
Celtic's strikers had come in for criticism following the club's poor Champions League campaign in which the Scottish champions scored only three times in six games.
Pukki in particular has struggled for form since joining the Parkhead club in the summer. The Finnish striker scored twice in his first two appearances but had failed to find the back of the net in nearly three months.
However, Pukki brought his long goal drought to an end in the 29th minute as he fired the Hoops in front.
Captain Scott Brown started the move as he threaded a ball to Joe Ledley whose first time cross into the box was tapped home from close range by the Finnish international.
Only a fine stop from Ben Williams denied Stokes a minute later as the keeper made a fingertip save to stop the Irishman's 25-yard thunderbolt from flying into the top left-hand corner.
Hibs failed to test Forster until the 43rd minute when the keeper had to be alert to get down low to stop a bobbling shot from just inside the box by Scott Robertson.
Hibs were showing guile in the second period and should have been level on the hour mark when slack play from Virgil van Dijk allowed Craig to rob the Dutch defender of possession in the box.
The Hibs captain then fired a fierce strike off the base of the post and Paul Cairney somehow failed to convert the rebound before the Celtic defence hacked the ball to safety.
Aberdeen moved up to fourth after beating St. Mirren 2-0 at home with Scott Vernon striking in the 20th minute and Barry Robson in the 60th.