When Scott McDonald left the field with seven minutes to go, the Parkhead crowd afforded him a tremendous reception, for his hat-trick had illuminated a game which would have had little to recommend it had the Australian not provided a lesson in finishing.

However it was the departure of another Celtic striker which caused some concern with the club's Champions League match against AC Milan in mind. Jan Vennegoor of Hesselink limped off in the first half after injuring himself in the process of shooting.

Gordon Strachan revealed the problem was the player's hamstrings and there was only "an outside chance" the Dutchman would be fit to play on Wednesday night.

Whether the Rossoneri defence will be quaking about facing a Celtic forward line led by a diminutive Australian is open to debate. But McDonald - always a bubbly individual - is certainly relishing the prospect.

"I'm full of confidence, I always am, but when you score a hat-trick - your first ever in senior football - it doesn't hurt going into a game against Milan," said the 24-year-old.

McDonald's strikes, which took his tally for the season to six, also took Celtic back to the top of the SPL table, albeit only on goal difference. But then, goals do make all the difference.

Had Jordan Robertson showed McDonald's appetite and accuracy, United may not have ended up on the wrong side of what looked like a hammering.

Twice at the start of the second half, the young striker had a chance to bring the Tayside club level. His first shot was nothing more than a pass-back.

His second, after a Lee Wilkie through ball had unlocked the offside trap, was directed far too close to Artur Boruc and the goalkeeper was in no mood to repeat the errors which cost Celtic dear at Easter Road last weekend.

Even after that, defender Darren Dods could have scored, steering a header wide of the far post, and all this action in and around Celtic's penalty box significantly happened before McDonald notched the second and third goals which secured the points.

His first came in the seventh minute, from about the closest range possible and only after United had been complicit in their own downfall. Maybe Craig Levein was at fault too, for once again - because of injuries - the United manager chose to deploy Barry Robson in the left-back position.

That compromise denuded United of the captain's drive in midfield and while Levein insisted Robson had coped admirably in that position in recent games, he was completely undone when Aiden McGeady skipped past him before standing up a delightful cross to the back post.

Vennegoor of Hesselink supplied the header and Grzegorz Szamotulski in the United goal only succeeded in parrying the ball up at a nice height for McDonald to nod it home.

Instead of inspiring Celtic, however, the early goal only seemed to make them sloppy and what with that, and United's lack of composure in possession, the first half had little to commend it.

Celtic did have chances also, most noticeably when Donati and McDonald exchanged passes in a swift break which ended with the Italian attempting a cute finish when the more rewarding ball may have been inside to an unmarked McDonald.

McGeady remained a joy to watch though, drifting off his right flank late in the first half to test United's Polish goalkeeper with a decent drive.

With Shunsuke Nakamura a major doubt for Wednesday, the young Irishman's form on the right side of midfield was encouraging as his final ball seems more accurate from his more natural side.

Levein recognised the need to change the pattern of play and introduced Steven Robb and Stuart Duff at the re-start, a reshuffle which allowed Robson to move into midfield and Willo Flood to switch to a more central area.

That tactical move seemed 45 minutes late, but it sparked United into their best period in the match. However there was no reward, not from Jordan Robertson or Dods, both of whom had chances they should have scored from.

Not that such opportunities indicated a sea of change in the general direction of play for Celtic were far more focused than they had been in the first half and should have already put United to the sword thanks to the energy and vision of McDonald. He twice teed up Killen only to see the substitute striker fail to convert.

Not that McDonald was disheartened, for that would be alien to his character. Instead he did what any good striker would do. He took matters into his own hands with two goals in five minutes.

Scott Brown burst between United centre-backs before rolling the ball into McDonald's path. The former Motherwell man still had plenty to do, but he shrugged off the attentions of Sean Dillon, rounded the goalkeeper and slid the ball into the net.

The goal that completed his hat-trick was started and finished by the man-of-the-match, who won back possession having lost it, and then flicked the ball out wide to McGeady. By the time McGeady crossed from the right, McDonald had made his way to the far post where he prodded the ball home from close range.

Celtic may have lost one striker yesterday, but McDonald has really found his shooting boots ahead of a date against Milan.

Celtic substitutes: Killen for Vennegoor of Hesselink 37, Sno for Donati 78, Zurawski for McDonald 83. Not used: Mark Brown, Kennedy, Riordan, O'Dea. Bookings: Hartley 64 Dundee United substitutes: Duff for David Robertson 45, Robb for Gomis 45, Cameron for Flood 61. Not used: McLean, Kerr, Kenneth, Russell. Bookings: Dods 24, Robson 67.

Referee: Dougie McDonald. Att: 57,006