Albian Ajeti scored his first Celtic goal to give the Hoops three valuable Premiership points against newly-promoted Dundee United at Tannadice.
After a goalless first half the visitors increased the tempo but a well-organised home side defended stoutly amid growing Hoops nerves.
However, in the 82nd minute Switzerland striker Ajeti, making his league debut as a second-half substitute following his recent £4.5million move from West Ham, repaid a chunk of that fee when he fired in what turned out to be the only goal of the game from 12 yards.
Celtic had returned to league action after missing the last two matches against St Mirren and Aberdeen through postponement after defender Boli Bolingoli breached coronavirus protocol and boss Neil Lennon will be pleased with the win. It keeps Celtic six points behind Rangers with two games in hand as they prepare to play Ferencvaros in their second Champions League qualifier on Wednesday night.
United, with Nicky Clark, Jamie Robson and 17-year-old Lewis Neilson back in the side, certainly showed no signs of trepidation.
Celtic defender Christopher Jullien stretched to concede an early corner which Neilson headed over.
The visitors had Jeremie Frimpong and Olivier Ntcham back in the side at the expense of Hatem Elhamed and James Forrest, and it was the former who used his pace to prevent Peter Pawlett getting a shot away against Celtic keeper Vasilis Barkas just 14 yards from goal.
However, the champions steadied and in the 12th minute French striker Odsonne Edouard struck the outside of Benjamin Siegrist's left-hand post with a drive from 12 yards after United skipper Mark Reynolds inadvertently redirected a Ryan Christie cross into his path.
An absorbing contest continued.
In the 32nd minute, after a swift United break, Ian Harkes set up Luke Bolton but from 16 yards he blazed the ball over the bar.
At the other end, Siegrist did well to parry Ryan Christie's deflected drive away from danger before blocking a close-range effort from Edouard with Mohamed Elyounoussi knocking the rebound wide.
Celtic came out for the second half fired up.
Within seconds of the restart Siegrist made a fine save from Christie's long-range drive with Jullien volleying the corner over, then the United goalkeeper thwarted Edouard when he tried to steer the ball in from eight yards.
The hosts refused to be subdued but Christie missed the target with another shot from 12 yards after being set up by skipper Scott Brown.
Celtic kept probing but Micky Mellon's side remained firm and indeed in the 68th minute Barkas was tested with a powerful drive from Jamie Robson after a swift counter.
In the 72nd minute Ajeti and defender Kristoffer Ajer replaced Ntcham and Greg Taylor as Lennon tried another route to victory.
Minutes later United's Calum Butcher fouled Edouard at the edge of the box and the striker skimmed the bar with his curled free-kick but the goal arrived soon afterwards.
Siegrist made yet another good save from Christie and Edouard did well to keep the ball alive before Ajeti drilled in a shot which ended in the roof of the net to take the points back to Glasgow.
