If Hearts fail to win the League, even with Rangers off the boil, they can hardly complain, having failed to win a game against either of the Old Firm this season. A win would have taken Hearts to the top, but they opted for organisation and deep defence to claim the point that at least preserves their ambition for another day.
Celtic could have stolen all the points a minute from the end of the game when Simon Donnelly, who came on in the 59th minute for the injured Jackie McNamara, saw his fierce shot from the edge of the area punched away cleanly by Gilles Rousset.
McNamara had been doubtful for the match after picking up an ankle injury while playing for Scotland against Denmark in midweek. Conversely, Craig Burley and Paul Lambert missed that 2-1 defeat through injury but were in the Celtic starting line-up.
Hearts, without Gary Locke who is recovering from a knee operation, made a positive start, with Stephane Adam's cross from the right causing panic in the Celtic defence. By contrast, Celtic found it hard to get going, and even though the Danish international Morten Wieghorst broke clear, he succeeded only in upsetting Rousset in the way he tangled with the goalkeeper.
The Glaswegians began the second half brightly, and Lambert and Alan Stubbs linked up to give the crowd a rare moment of excitement. The Celtic central defender Stubbs picked out Henrik Larsson, but the Swede overran the ball and Steve Fulton was able to hack it away.
With Harald Brattbakk subdued after a number of stiff challenges from David Weir and Stefano Salvatori, it was little surprise when he was replaced by Darren Jackson with 25 minutes to go.
The challenges were coming in thick and fast, so there was little time or space for creativity, although Donnelly gave Celtic the spark they were lacking. Hearts, however, dug in and preserved their hard-won point.