The Australian international gave the champions the lead after seven minutes and added a double in the second half after the Parkhead men had survived some nervy moments.

McDonald's hat-trick helped the defending champions leapfrog rivals Rangers on goal difference, but the victory came at a price for Strachan as big Dutchman Jan Vennegoor of Hesselink limped off before the interval with a hamstring injury.

The Socceroo revealed it was his first hat-trick as a professional but his delight was tempered by the news that his strike partner is likely to be missing against AC Milan.

The former Motherwell player said: "It was my first senior hat-trick so it was something special and I will treasure it the rest of my life. Hopefully there will be more to come from me in my time at Celtic.

"I will get all the boys to sign the ball and put it somewhere in the house where everyone can see it. But I won't be putting it on ebay - no chance of that!"

He added: "Losing Jan would be a big blow to the team. He has scored quite a few goals and has a big reputation on the continent.

"I'm sure AC Milan will be happy if he is missing."

Gordon Strachan's men sit at the top of the table on goal difference as they look forward to Wednesday's Champions League clash with AC Milan at Celtic Park.

The match ended in a comfortable win for Celtic and they will be buoyed for the visit of the Serie A giants but there was little indication in the first half that the win would be attained so easily.

Rangers' draw at Motherwell earlier in the day meant Celtic knew victory over United would take them back top of the SPL.

McDonald's goal should have infused Celtic Park with enthusiasm but in fact it had the opposite effect.

Aiden McGeady easily skinned United skipper Barry Robson on the right-hand side of the box and stood his cross up at the back post for Jan Vennegoor of Hesselink.

The big Dutchman powered in a close-range header which United keeper Grzegorz Szamotulski did well to parry but the little Australian international bundled the rebound over the line from less than a yard out.

Surprisingly, the goal brought a nervousness to the home side and United enjoyed a spell of possession and pressure although Celtic goalkeeper Artur Boruc was not called in to action.

The tempo dipped at the halfway point of the first 45 minutes and it was referee Dougie McDonald who was raising the temperature the most with some baffling decisions.

In the 34th minute, McDonald and Massimo Donati played a one-two past United stopper Lee Wilkie as Celtic broke on the counter but the Italian midfielder's chipped shot from the edge of the box, which Szamotulski saved easily, riled the home fans who obviously expected a better end product.

Chris Killen replaced the injured Vennegoor of Hesselink in the 37th minute but it was McGeady who came closest to getting number two when his left-footed drive from 20 yards drew a fine save from the United goalkeeper.

For the second half, United boss Craig Levein brought on Steven Robb and Stuart Duff for David Robertson and Gomis, moving Robson in to the centre of midfield in his reshuffle.

In the 52nd minute the Parkhead side should have doubled their lead after good work by McGeady and Doumbe wide on the right.

When the ball landed at the feet of McDonald inside the United penalty area he swiftly moved it on to Killen but from 14 yards out the former Hibernian striker all too casually stroked the ball past the post.

Moments later, as the game swung from end to end, Celtic midfielder Scott Brown drove a cross to the back post but the sliding Killen arrived too late to capitalise.

In the 55th minute it was United's turn to be profligate after Lee Wilkie's pass had split the Celtic defence open and let Jordan Robertson with a one-on-one with Boruc.

The United striker strode through with purpose but blasted his low drive against the legs of the diving Poland international and the ball flew to safety.

Nerves inside Celtic Park continued to jangle and in the 64th minute a Robson corner from the right found Darren Dods at the back post but the lanky defender somehow headed past from barely three yards out.

But McDonald eased those nerves in the 66th minute when he grabbed a second goal.

The little striker latched onto a Brown pass inside the United penalty area, shrugged off the attentions of United full-back Sean Dillon, rounded Szamotulski and slotted the ball in from a tight angle. It was all over for United.

In the 71st minute McDonald grabbed his first hat-trick for the Hoops when he knocked home McGeady's deep cross from six yards out, thus doubling his tally at Parkhead since signing from Motherwell in the summer.

Brown volleyed just wide from the edge of the box as United's resilience melted.

In the 81st minute McDonald was given a standing ovation when he was replaced by Maciej Zurawski but again it was McGeady who came close, stinging Szamotulski's fingers with a 20-yard drive.

Milan are sure to offer a tougher test on Wednesday but at least Celtic showed today they can conjure results when performances are not top notch.