Charlie Mulgrew's injury-time equaliser denied Dundee United their first away win against Celtic in over 20 years.
United's Stuart Armstrong lifted the ball over Fraser Forster late in the first half after latching onto Nadir Ciftci's wonderful pass.
Anthony Stokes and Amido Balde squandered several chances for Celtic.
Brian Graham should have doubled United's lead before Mulgrew headed home at the death to keep the hosts' unbeaten league run this season intact.
It was April when Neil Lennon's side last lost in Scotland's top flight and they came within 60 seconds of tasting league defeat again, but Mulgrew's third goal of the season preserved their record.
The last time Celtic were unbeaten in the league after their opening 11 games was 2003.
Despite their profligacy up until Mulgrew's leveller, the Scottish Premiership leaders can take heart from digging deep late on as they prepare for their Champions League clash with Ajax in Amsterdam on Wednesday night.
Dundee United will rue the chance that fell to Graham from Ciftci's cross just after the hour-mark, when the former Raith Rovers striker miscued a header from three yards.
Jackie McNamara's men drop to sixth in the Premiership in light of St Johnstone's away win at Tynecastle against Hearts.
Stokes signed a three-year extension to his contract during the week, but could not celebrate that with a goal at Celtic Park, volleying over the crossbar from the edge of the box and then directing a Mulgrew free-kick over with his head.
Portuguese striker Balde also spurned first half opportunities, while Hoops keeper Fraser Forster was called upon to thwart Gary Mackay-Steven and Graham.
United did make the breakthrough, though, and it was an excellently crafted counter-attack.
Armstrong timed his run perfectly to latch on to a delightfully lofted Ciftci pass and the Scotland Under 21 international rounded Forster before lifting it into the net - the second time in consecutive visits that Armstrong has scored at Celtic Park.
United goalkeeper Radoslaw Cierzniak did well to block James Forrest's drive and Stokes was unsuccessful with further efforts before the break.
The home crowd's frustration grew as they grateful watched Graham waste his fantastic opportunity, before Stokes tested Cierzniak again at his near post.
But, as is always the case at Celtic Park, anything can happen right up until the final whistle and the late twist came when Mulgrew got his head on Izaguirre's delivery.
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