It was a game which saw the Hoops overcome a dogged United performance and one in which their midfield supremacy eventually won the game.
The Tangerines had started the better with good opportunities falling for David Robertson and Noel Hunt.
Gradually however the league leaders eased themselves into the game and should have scored in the 20th minute when Jiri Jarosik recklessly blasted over from only ten yards.
United however were very much matching their visitors and big Lee Wilkie missed a clear chance in the 29th minute. From only two yards out the defender headed wide as he touched on David Robertson's curling corner.
As the half progressed there was plenty of effort as both teams effectively cancelled each other out and it looked as if it would require something special to break the deadlock.
Captain Barry Robson almost did it in the 38th minute with a 25-yard rocket which flew off the face of the bar.
Then two minutes later at the other end, the departing Grzegorz Szamotulski produced a 'Gordon Banks' save with a one-handed stop from Gary Caldwell turning the ball down and up on to the bar.
The Celts moved up a gear in the second period opening with a cracking move which should have ended with a goal. Following a mistake from Robson, Aiden McGeady was off like a greyhound, eventually setting up Scott McDonald who dragged the ball wide when it seemed easier to slot it home.
But the pressure was eventually rewarded with a headed goal from Jan Vennegoor of Hesselink. An excellent corner from Paul Hartley was met by a lovely flick which went in off the post.
It was game over a few minutes later although there was a suspicion of handball from Stephen McManus. Another dead ball from Hartley was missed by everyone but the big defender was at the far post to bundle it in.
And it was nearly number three three minutes later when Darren Dods almost headed the ball into his own net from a McGeady corner and with the Hoops in total command, Scott Brown rattled the post with a 12-yard strike.
With time running out for the Tangerines, Wilkie had an 86th minute header easily saved by the keeper, then both Jordan Robertson and Willo Flood missed easy opportunities which demonstrated the difference between the two sides in taking their chances.