Gary Hooper and James Forrest both hit the woodwork for the home side, but it was an afternoon of frustration against a side the Hoops had beaten 4-1 in the Scottish Communities League Cup quarter-finals in midweek.
With Rangers winning 2-1 against Aberdeen at Pittodrie earlier in the day, Celtic's title hopes took another battering and although they have a game in hand, the fans who booed them off at the end will have little faith in the Parkhead men recovering.
Celtic turn their attention to the Europa League and the visit of Rennes on Thursday night and manager Neil Lennon will wonder just what he will get from his team, who have showed the best and worst of themselves in recent games.
Certainly there can be no complaint about the result as Hibs were more than worthy of a point.
As expected, Charlie Mulgrew was restored to the Celtic defence after recovering from an ankle injury as Daniel Majstorovic dropped to the bench, although right-back Mark Wilson kept the captain's armband.
Hibs boss Colin Calderwood made four changes to the side which had been so outplayed in the second half in midweek.
Goalkeeper Graham Stack, Sean O'Hanlon, Danny Galbraith and Lewis Stevenson came in for Mark Brown, Ian Murray, Victor Palsson and Ivan Sproule.
The game was something of a slow burner. In the ninth minute Hoops goalkeeper Fraser Forster had to race outside his box to head clear and thwart Leigh Griffiths.
Moments later Stokes had a drive from the edge of the box saved by Stack at the second attempt.
In the 27th minute there was a moment of excitement when Hibs left-back Paul Hanlon slipped, allowing Stokes to get away down the right, but when the Irishman's driven cross came into the box it bounced off Hooper and went straight to Stack.
Celtic stepped up the pace momentarily and Stokes drove into the box from the other wing but his low angled drive was blocked by Stack.
It was not vintage Celtic by any standards but in the 36th minute Hooper worked a clever one-two with Stokes at the edge of the box to leave him through against the Hibs keeper.
However, although the Englishman's right-footed shot beat Stack, the ball flicked the outside of the post and went wide.
Forrest, who had scored twice in the midweek win in Leith, came to life five minutes from the break with a decent right-footed effort from distance which drew a good save from Stack, with no Celtic player close enough to take advantage of the loose ball.
Two minutes after the break, after midfielder Ki Sung-yueng had fouled Gary O'Connor 30 yards from goal, Forster was called in to action to save Galbraith's free-kick, which was too straight to cause real concern.
Mulgrew fouled O'Connor closer to goal in the 49th minute as the striker drove at the box, and this time Griffiths sent a volley just past the post after taking a short pass from David Wotherspoon
Griffiths then caused more problems as he slipped past Mulgrew on the byline and his cut-back found Galbraith, whose drive was deflected for a corner which Celtic nervously survived.
The Easter Road side were working their way up the pitch far too often and too easily for the home fans, who let their feelings be known.
In the 64th minute Forrest made space for himself 25 yards out and his shot beat Stack but clipped the top of the bar on the way over.
In the 71st minute Lennon replaced Ki with Paddy McCourt and Beram Kayal with Victor Wanyama, before Sproule replaced Junior Agogo and Matthew Thornhill came on for O'Connor.
Still, Celtic could not get on top and with seven minutes remaining Georgios Samaras replaced Hooper, but in the 87th minute it was Sproule who came close with a drive from the edge of the box after stepping inside Mark Wilson with some ease.
In the closing stages Stokes drove wide from 20 yards with an unconvincing effort which summed up the Hoops performance.