Craig Bellamy fired Celtic back to the top of the Bank of Scotland Premier League with a terrific hat-trick at Tannadice.
Any hopes Dundee United interim-manager Gordon Chisholm had of a debut result following the sacking of Ian McCall were shot down in flames by Celtic Park's new hero.
The Wales striker produced three red-hot finishes and, although the home side twice equalised through Jim McIntyre and Barry Robson, Bellamy fired the champions two points clear of Rangers going into the international break.
Celtic manager Martin O'Neill made one change with Stanislav Varga recovering from a mystery illness to replace Stephane Henchoz in the only change to the starting XI which won at Inverness Caledonian Thistle on Wednesday.
Chris Sutton was handed a place on the bench after a hamstring problem.
But the Glasgow giants were bracing themselves for a backlash from the bottom club after the sacking of McCall on Monday.
Interim-boss Chisholm made two changes from the team which crashed to Kilmarnock last weekend. Derek McInnes and James Grady were relegated to the bench with recalls for Mark Kerr and Robson.
The home side were given a warning of what was to come in the fifth minute when the in-form Bellamy was inches away from pulling down Varga's free-kick in the area.
But United were severely punished for leaving the Welshman alone just seconds later as Celtic made the dream start.
The on-loan striker made a run out to the right, was found by Jackie McNamara and then he steadied himself on the corner of the penalty area before letting fly with an unstoppable right-footed drive which flew past the hand of Tony Bullock and into the top corner.
Scotland number one Robert Douglas was booked moments later for handling a Varga back-pass but the Celtic wall charged down Alan Archibald's strike from the edge of the box.
United produced a great passage of football in the 21st minute which deserved an equaliser. Crawford played a great reverse pass into the path of Robson and he picked out Stuart Duff in the area and he blasted a volley just over the crossbar.
Bobo Balde could have silenced the home crowd in the 24th minute but he headed Thompson's free-kick straight at Bullock.
But it was the goalkeeper's quick-thinking which brought their leveller against the run of play. He immediately launched a kick downfield, catching the Celtic defence by surprise, and McIntyre latched onto it to drive the ball
past Douglas.
However, Bellamy produced an even better finish in the 34th minute to put the champions back into the lead.
Ulrik Laursen ran with the ball from his own half and picked out the clever run of the Wales striker behind the United defence and he wasted no time in crashing a left-foot strike past the stranded Bullock and into the back of the net off the inside of the upright.
Varga could have extended the lead just before half-time but Bullock pulled off a great save to his left to save the defender's point-blank header.
Chisholm made a change in the 57th minute by bringing on McInnes for Kerr before O'Neill brought on Sutton for Hartson, who has been struggling with an ankle problem.
And Robson levelled matters after 71 minutes, capitalising on a Lennon mistake and finding the top corner from the edge of the area with a spectacular shot.
Chisholm threw on Grady for Crawford in the 75th minute as he went in search of a United win.
However, Bellamy looked the man most likely to produce a winner and he held his head in his hands after he had he controlled Sutton's pass with his back to goal.
He brilliantly deceived Ritchie to lose his marker but then screwed his left-foot shot just past the upright.
But the striker was on fire and he did see his next shot hit the back of the net - for his hat-trick and his sixth goal in seven starts - to put the champions back in front.
Sutton flicked on Douglas' long punt downfield and Bellamy pulled the ball out from under his feet before hitting a right-foot shot past Bullock from just inside the area.
There was some bad news for Celtic as Sutton limped off late on after O'Neill had used up his three substitutes to give him some anxious late moments.
United also went down to 10 men when Brebner was stretchered off in injury time before Douglas pulled off a stunning one-handed save to keep out Robson's free-kick from the edge of the area.
Teams
Dundee Utd Bullock, Wilson, Kenneth, Ritchie, Archibald,
Duff (Scotland 86), Kerr (McInnes 58), Brebner, Robson,
Crawford (Grady 76), McIntyre.
Subs Not Used: Colgan, Samuel, Dodds, Robertson.
Booked: Kenneth, Brebner.
Goals: McIntyre 24, Robson 71.
Celtic Douglas, McNamara, Balde, Varga, Laursen (Wallace 78),
McGeady (Henchoz 84), Petrov, Lennon, Thompson, Bellamy,
Hartson (Sutton 61).
Subs Not Used: Marshall, Valgaeren, Fernandez, Maloney.
Booked: Douglas, McNamara.
Goals: Bellamy 5, 34, 80.
Att: 10,828
Ref: D McDonald (Scotland).