Scott Sinclair’s controversial penalty with two minutes left extended Celtic’s unbeaten domestic run to 66 games as Motherwell were denied a historic win.
Mikael Lustig’s own goal in the 78th minute, diverting Craig Tanner’s free-kick, threatened an upset.
But when Callum McGregor went down after an Andy Rose challenge, Sinclair kept his nerve to send the spot-kick high into the left corner.
Well keeper Trevor Carson had earlier denied McGregor and Kieran Tierney.
It was the closest Celtic have come to defeat since their last loss to Scottish opponents – against St Johnstone – back in May 2016.
But a point was enough to extend their lead at the top of the Scottish Premiership to four points, with a game in hand, after Aberdeen’s 3-0 defeat at Rangers.
Motherwell knew if they were to stand a chance of stopping the Celtic steamroller, they would have to turn the match into a battle and they did just that from the first whistle.
They pressured and fought the visitors over every blade of the Fir Park pitch, trying to knock Celtic out of their stride, and looked comfortable in possession but chances were scarce.
In response Celtic were forced to make quicker passes and at times they looked more frantic than they wanted to be.
They also suffered an early blow when Patrick Roberts pulled up with a hamstring problem that will require a scan, and makes him a doubt for the Champions League visit of Anderlecht next Tuesday.
Callum McGregor was the first to find a gap and his fierce shot was well saved by Carson after impressive build-up play involving Leigh Griffiths and Tom Rogic.
They had their goalkeeper to thank for going into the interval on equal terms after he pulled off a fabulous stop from Tierney.
The Celtic left-back blasted low from six yards out after mesmerising one-touch build-up play carved the hosts’ defence open, but Carson somehow got an arm to the effort and the ball flew over the bar.
Tierney was involved again minutes after the restart after sprinting clear of Richard Tait on the left flank, but Griffiths couldn’t convert his inch-perfect cross. James Forrest pounced on the resulting block but his effort was also denied by a ruck of lunging Motherwell defenders.
Carson then dived low to deny McGregor after the midfielder let fly with another powerful effort. It was beginning to feel all very familiar.
Motherwell refused to buckle though and Louis Moult had a chance from eight yards out after a mix-up in the Celtic defence, but the striker snapped at the effort and it sailed over the bar.
As the game became more stretched, McGregor – again – and Griffiths both watched chances flash just wide.
But space was opening up at the other end and substitute Craig Tanner passed up a golden opportunity with a wayward header after a great cross from Chris Cadden.
But with 11 minutes left, they took the lead courtesy of a Celtic player. Tanner flighted in a free-kick from 40 yards out and Lustig stretched to clear but instead turned it past the helpless Craig Gordon.
Fir Park erupted as the home fans realised their side was on the verge of blowing away their Hampden blues and creating history.
As the champions threw everything forward, Tom Rogic watched his effort bounce off the base of the post and back into Carson’s arms.
Then after Carson pulled off another fabulous stop, McGregor went down inside the Motherwell box under the challenge of Rose and referee Willie Collum pointed to the spot. The home fans were furious but up stepped substitute Sinclair to fire it home.
He wheeled away with his finger to his lips, aimed at the Motherwell fans who had been calling him “cheat” for winning a controversial penalty in Sunday’s League Cup final against the same opponents.
The travelling support rose to their feet and bounced in unison and relief. Record intact – just.