Hat-trick hero Giorgos Giakoumakis turned Celtic's saviour to sink resilient Dundee with a dramatic late winner.
Ange Postecoglou's side cut it fine to stretch their Premiership lead over Rangers to three points in a five-goal thriller with the Premiership's bottom side.
Mark McGhee very nearly opened his unfancied Dens Park reign with a draw in Glasgow but the Greek striker struck with just minutes remaining to claim all three points.
Dundee had led through Danny Mullen early on before Giakoumakis produced a quick-fire double to turn the match on its head.
But Ryan Sweeney pegged Celtic back again, popping up with a powerful header to set up a grandstand finish that was eventually settled by Giakoumakis.
Victory pushes Postecoglou's team further clear of the reigning champions after they slipped up to draw at Tannadice earlier on Sunday.
The Celtic boss recalled Giakoumakis and Reo Hatate after a midweek Europa Conference League defeat while McGhee was without injured captain Charlie Adam.
His five at the back setup ensured it didn't take long for proceedings to fall into the expected pattern, with blue shirts setting up camp on the edge of their own box.
Celtic pushed and probed and it took around 20 minutes to some excitement around Parkhead as Reo Hatate controlled a high ball and looped an effort over Ian Lawlor's crossbar.
What it needed was proverbial cat among the pigeons to either entice Dundee out or elevate Celtic's sense of urgency.
The latter may have been the outside bet but it was Danny Mullen who stunned Celtic Park into silence as he swept home Paul McMullan's corner at the back post.
Now was the time for the Dark Blues to really dig in but within 14 minutes they were not only level, but behind.
Giakoumakis, a peripheral figure until then, suddenly took centre stages and he volleyed home on the swivel from 10 yards before stabbing home Daizen Maeda's low cross just four minutes later.
Celtic Park had certainly livened up, but suddenly it was fury sweeping across the stands as two claims for penalty were waved away.
The first was debatable as Jordan McGhee made a hash of an attempted clearance, but the second looks as clear cut as is possible when Vontae Daley-Campbell smashed into Giakoumakis as the ball found Maeda at the back post.
Referee Gavin Duncan was unmoved, however, and Dundee reached the interval just a goal adrift.
The second period looked destined to play out as a 45 minute attack vs defence drill until Niall McGinn delivered an enticiing free-kick for Sweeney surge between Cameron Carter-Vickers and Carl Starfelt to brilliantly head home.
Postecoglou didn't waste time ringing the changes, withdrawing Hatate and Maeda for Tom Rogic and Liel Abada as the home side tooled up for a siege offensive.
Jota, as ever, was in the thick of it - flashing a cross along the face of goal before testing Lawlor with a low shot.
It was agonising for the hosts but just as time appeared to be running out, Giakoumakis popped up at the near post to have the final say.
Giakoumakis the hero
The Greek striker will have been disappointed to miss out on a starting berth against Bodo/Glimt in midweek and he set about putting that right here with a stunning treble.
Dundee's resolve had been hardened by Mullen's surprise strike and the key for Celtic then was not to allow their visitors to sit on a lead for anything length of time.
Giakoumakis' first was an excellent finish on the spin and the second was a typical striker's goal, anticipating the ball at the front post and stabbing home.
The third was pure desire as he muscled his way onto a front post cross to head home and set Celtic Park alight.
As there remains no sign of an imminent Kyogo Furuhashi return, the onus has been on Giakoumakis to fill that void and he certainly delivered on Sunday afternoon.
Decisions in focus
Rangers left Tannadice earlier this afternoon believing they should have had at least one penalty and there was a similar feeling here for their city rivals - albeit not with the added sting of dropped points.
Both incidents here arrived with seconds of one another and had Celtic fans and players up in arms.
The first, for an alleged handball, would've been harsh on Jordan McGhee but there was little doubt about the second.
Daley-Campbell absolutely wiped out Giakoumakis and the only explanation for the non-award, surely, would be the referee attempting to play advantage to Maeda at the back post.
Even so, it was a real surprise Duncan did not bring it back for a spot-kick afterwards.
Dundee refuse to go away
It's been a week of mostly gloom on the blue half of the City of Discovery, with little in the way of optimism surrounding McGhee's surprise appointment.
But. like their manager in his pre-match interview, there was an air of defiance about the men in blue as they came agonisingly close to securing a priceless point.
With St Johnstone seemingly on the rise following their win over Hearts, it was important for Dundee to combat the narrative that the tide is turning at the bottom.
They couldn't quite hold out, but McGhee will be encouraged by the fact his players are clearly up for the fight.
