A blistering three goals in six minutes of the second half helped Celtic increase their lead of the SPL at Tannadice.
Having produced a steady resistance in the first half, the Tangerines crumbled under the pressure and were comprehensively beaten in the end.
United had begun the more determined outfit. Referee Kenny Clark came to the rescue of the visitors in the sixth minute when he controversially awarded a foul against Jim McIntyre as Billy Dodds knocked the ball into the net at the far post.
With slippery conditions underfoot, it looked increasingly likely that a mistake would perhaps lead to the first goal and that's what happened in the 34th minute.
Chris Innes slipped as he tried to clear the ball from Henrik Larsson and the ball fell to the feet of Chris Sutton who coolly shielded David McCracken and curled a low 15-yard shot into the corner of the net.
Five minutes from the break, referee Clark yet again showed worrying inconsistency when he failed to punish Stanislav Varga with a second yellow after booking Innes for an identical foul a few minutes earlier. It incensed the United supporters and players alike.
It took Celtic only six minutes of the second half to begin the destruction. A Stilian Petrov corner saw Alan Archibald stargazing giving Larsson the opportunity to bullet his six-yard header high into the net - his 15th goal of the season.
It was three in the 55th minute with a somewhat freak goal. Larsson's overhead kick from 25 yards caught out the keeper. As he back-pedalled, he tipped the ball onto the bar for Sutton to run in and tap the ball home from two yards.
Celtic were now running riot and it was four two minutes later with a fantastic second goal from Larsson. Petrov laid the ball into the path of the Swede and he let fly high into the corner from 20 yards.
With the game over, McIntyre grabbed a consolation goal with a 16-yard deflected shot off Johan Mjallby that gave Rab Douglas no chance.
But the Celts had the final say when Archibald tripped Sutton in the 80th minute and the striker took the penalty himself sending the ball high into the net for his hat-trick.