The Glaswegian side remain third in the table, with Motherwell in second, and the pressure on manager Neil Lennon will likely increase as they fell further behind the Gers, who beat Aberdeen 2-1.
Hibs, on the other hand, will be pleased to have held the hosts to a draw, having been beaten 4-1 by them midweek in the League Cup quarter-final.
The away side showed their attacking intent early on when Fraser Forster, on-loan from Newcastle United, had to race out his box and head clear to prevent opposition striker Leigh Griffiths from capitalising.
Hibs striker Garry O’Connor let a number of chances go begging throughout the game, and squandered the best chance of the first half by somehow sliding the ball wide of the right-hand post after passing the keeper one-on-one.
Celtic's James Forrest hit the crossbar for the home side from 20-yards out but they were still unable to make the breakthrough against a resilient Hibs outfit.
Gary Hooper, who is attracting attention from Premier League clubs, made a mess of his chance for the Celts, adding to the negative mood inside the stadium as the team desperately searched for momentum.
The visitors' goalkeeper, Graham Stack, saved Anthony Stokes’ drive from outside the box early in the second half.
O’Connor had another opportunity for Hibs with 20 minutes remaining, running at the Celtic defence on the counter-attack but hit his shot over the bar after failing to run off three defenders.
The home fans at Celtic Park became restless as the game went on, with most of the game’s best chances coming from long-range efforts for Lennon's side.
Stokes could have given the hosts the win late on with a shot from outside the box, but that was typical of a game that lacked many clear-cut chances for either side.