Shunsuke Nakamura and Scott McDonald hit the woodwork in the first half before United midfielder Craig Conway missed a sitter from six yards out when he headed over with only Artur Boruc to beat.
The Hoops dominated the second half but could not find a way past a resolute Tannadice defence who now look forward to Sunday’s CIS Insurance Cup final against Rangers at Hampden.
The jeers rang out around Celtic Park at the final whistle with the realisation that the Ibrox club are three points ahead and with a game in hand as the SPL title race hots up.
Celtic’s domination of the first half began from the first sound of Mike McCurry’s whistle.
In the third minute midfielder Aiden McGeady crossed from the left to find McDonald who helped the ball on to the unmarked Nakamura at the back post.
The Japan international carefully curled his low, left-footed drive from 14 yards past United keeper Lukasz Zaluska but watched the ball clip the outside of the post before speeding past.
As Celtic took a firmer grip of the game, Nakamura turned provider when he skipped past Danny Grainger on the right to throw the ball up to the back post where the stretching Georgios Samaras headed over the bar.
But in the 38th minute the visitors should have taken the lead when Kovacevic’s cross from the right found Craig Conway six yards from goal.
The midfielder somehow headed over the bar with just the keeper to beat and held his head in frustration.
From cruising through most of the period, Celtic wobbled in the closing few minutes of the first half, their fans not slow to express their displeasure.
However, inspired by McGeady who was having another fine game, the champions took the initiative immediately after the restart.
In the 53rd minute Nakamura’s whipped-in free-kick from the left was flicked on by the head of Brown through a ruck of players in the six-yard box but found no takers.
United, growing in confidence, had a more than decent penalty claim when Robson appeared to charge down Prince Buaben’s drive with both hands inside the Celtic penalty area.
As the tension mounted, McManus had a low drive saved by Zaluska and then McDonald went down rather too easily in the United box after brushing past United stopper Garry Kenneth.
With five minutes remaining Vennegoor of Hesselink drew a good save from Zaluska seconds before he headed a Nakamura cross over the bar from eight yards out.
Boruc, Hinkel, Caldwell, McManus, Naylor, Nakamura, Scott Brown, Sno (Robson 62), McGeady, McDonald, Samaras (Vennegoor of Hesselink 62).
Zaluska, Kovacevic, Wilkie, Kenneth, Grainger, O’Brien, Robertson (Flood 75), Buaben, Kerr, Conway (Daly 83), De Vries (Hunt 77).
M McCurry (Scotland).um (Scotland).
Colin Nish boosted Hibernian’s UEFA Cup hopes with the only goal of their Premier League clash against European rivals Motherwell.
Nish cut through the heart of the Motherwell defence before slotting home as Hibs increased the pressure at the start of the second half.