Under the eye of new boss Pedro Caixinha, given a watching brief after signing a three-year deal yesterday, Rangers started brightly.
Their interim head coach Graeme Murty made two changes to his defence in his final match in charge, recalling Danny Wilson and Lee Hodson for Jon Toral and the suspended Rob Kiernan.
Martyn Waghorn squandered the game’s first big opportunity in the 24th minute.
He capitalised on a mistake by Dedryck Boyata, but his shot was diverted to safety by the left foot of Craig Gordon.
James Forest teed up his team-mate to fire home from the edge of the penalty area.
Celtic had the chance to double their lead shortly after the break when Callum McGregor, who replaced Nir Bitton at half-time, snatched at his volley from Kieran Tierney’s cross.
The champions searched for a second goal as Wes Foderingham twice saved from Armstrong.
And, with time ticking away, the visitors finally made their pressure count in scrappy fashion through Hill.
The English defender reacted quickest after yet another fine Gordon save kept out Emerson Hyndman’s low drive.
There was still a final opportunity for Celtic to snatch victory in stoppage time, but referee Madden turned down Griffiths’ appeal for a spot-kick.
It is just the second time this season Rodgers’ side have failed to take maximum points, but the draw extends their unbeaten run to 36 domestic matches stretching back to May last year.