Celtic came from two behind to draw with Dundee United and end 2006 unbeaten on their home soil in the Scottish Premier League.
David Robertson put Dundee United ahead
David Robertson headed United into a surprise lead from close range after 17 minutes against the league leaders.
Collin Samuel fired home following a Barry Robson free-kick.
But Darren O'Dea headed home after a free-kick from Shunsuke Nakamura, who then chipped in a beautiful equaliser to deny United victory.
They had been 12 minutes away from recording their first win at Celtic Park since Boxing Day 1992.
Evander Sno had replaced the suspended Neil Lennon in Celtic's midfielder after the captain's sending off against Falkirk on Saturday.
United were without the injured Steven Robb, while David Goodwillie dropped to the bench as David McCracken and Grant Smith came into the starting line-up.
Nakamura drove the ball inches past the far post as Celtic carved out the first good chance.
But the visitors took the lead when Lee Mair's cross to the back post was met by Robertson, who planted his close-range header past goalkeeper Artur Boruc.
Mair came to United's rescue when his perfectly-timed block tackle on Maciej Zurawski denied the Poland striker a certain equaliser.
Bobo Balde was stretchered off before half-time
Robson almost added to growing frustration inside Celtic Park when his curling shot from the edge of the penalty area went just a foot over the crossbar.
More woe visited the champions in the 37th minute when defender Balde injured his leg over-stretching to clear at the edge of his own box and had to be stretchered off.
The loss of the Guinean appeared to dampen the home side's enthusiasm and United started the second half with confidence.
Boruc did well to block an effort from Grant Smith before United went two ahead.
Samuel was first to react after a Robson free-kick was headed on by Garry Kenneth and Conway stabbed the ball into the six-yard box for the Trinidad & Tobago international.
Riordan was denied by an outstanding Stillie save, the United keeper diving low to his left to turn the Celtic midfielder's right-footed drive from 12 yards past the post.
But a dramatic two-minute spell brought the home side back into the game.
O'Dea knocked home a Nakamura free-kick from six yards after 78 minutes.
And the home side were level when the Japanese midfielder took a Riordan pass and floated a delightful chip from 20 yards over the despairing Stillie.
Celtic pressed hard for the winner and, in injury time, Riordan's effort from outside the box hit the post before rolling to safety with Stillie well out of his goal.
Celtic: Boruc, Telfer, Balde (O'Dea 39), McManus, Naylor, Nakamura, Sno, Gravesen, McGeady (Riordan 61), Zurawski, Jarosik (Miller 56).
Subs Not Used: Marshall, Conroy, Beattie, Pearson.
Goals: O'Dea 78, Nakamura 80.
Dundee Utd: Stillie, Conway, Kenneth, Mair (Proctor 85), Duff, McCracken, Kerr, Smith (Cameron 84), Robertson, Robson, Samuel.
Subs Not Used: McLean, Archibald, Easton, Goodwillie, Watson.
Booked: Robertson, Kerr, Robson.
Goals: Robertson 17, Samuel 58.
Ref: B Winter