Livingston goalkeeper Max Stryjek earned his side a share of the spoils at Celtic Park thanks to an injury-time penalty save against the Hoops.
The Lions had produced the type of battling defensive performance that has been their signature since their return to the top flight but they almost came undone in the final stages.
Ayo Obileye saw red in the second minute on injury-time for lashing out at Celtic substitute Kyogo Furuhashi to hand the hosts the perfect opportunity to claim all three points at the death.
But the Polish stopper got down low to his right to save from Giorgos Giakoumakis to earn his side a point and make it four games unbeaten for the visitors.
Remarkably, it was the sixth time in the 12 league meetings between the sides in which Celtic have failed to score.
As expected, Ange Postecoglou's men controlled possession but Livi proved difficult to break down with the Hoops only able to muster two shots on target.
Celtic would pepper the away side's box with deliveries that were comfortably dealt with as half-chances from Josip Juranovic, Liel Abada and Carl Starfelt were all that came of the first half - before Jack Fitzwater was in the right place to head an Anthony Ralston shot off the line.
The second half followed the same pattern with Livi frustrating their hosts, who lacked a cutting edge.
The West Lothian outfit had appeals for a penalty turned down five minutes from time as Joe Hart collided with Obileye as he raced out to clear a free-kick - before the Celts were awarded a spot-kick a few minutes later for the defender's petulance.
Stryjek would come to his rescue, though, with the save while Giakoumakis would squander a late effort at the back post as he looked to make amends.
Results elsewhere meant the Lions dropped to 10th in the table but they sit just three points off fifth place in a congested top flight.
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