Afterwards Bhoys boss Martin O'Neill acknowledged: "It was a great game, plenty of excitement and a game we deserved to win."
But all the plaudits went to the Welsh striker for an exceptional performance. "He was fantastic. It was outstanding goals from an outstanding player," said O'Neill, who was correct in his assessment although his team perhaps were slightly fortunate to shade it.
After the departure of Ian McCall following the dismal showing against Kilmarnock which took United to rock bottom, assistant Gordon Chisholm was promoted to acting manager.
His first decision was to drop captain Derek McInnes to the bench after his recent ineffective performances along with James Grady, who had been guilty of a poor finishing in past games.
It proved to be the right decision as his troops put on a splendid fighting display.
"I thought the boys gave tremendous effort and in all honesty I thought they deserved something," said Chisholm. "They showed the commitment I asked and I feel sorry for them."
With Celtic having come back into a strong run of form recently, the question around the ground before kick-off was 'how long could United hold the visitors?'
It was no surprise when the first chance and first goal fell to Celtic with a thundering strike from Bellamy in only the fifth minute. He ghosted in from the right wing, took Jackie McNamara's cross-field pass and powered a 14-yard shot high into the net.
The Tangerines took the setback on the chin and responded immediately with Steve Crawford's ten-yard shot flying narrowly over.
Then Bhoys keeper Rab Douglas was penalised and subsequently booked for dissent when he picked up a pass back, but the visiting defence blocked well.
The main threat continued at the other end. With 14 minutes on the clock, Bellamy almost snatched another when he left Paul Ritchie trailing, but his angular shot went narrowly wide.
This was followed by Alan Thompson's 30-yard pile-driver which Tony Bullock did well to hold at the second attempt.
Despite being under pressure, United continued to plough away and created two good chances around the 20th minute with Stuart Duff volleying over after an excellent four-man move, before the same player forced a full length dive from the keeper.
Jim McIntyre, however, went one better in the 24th minute when he latched onto a Bullock goal kick, beat Stan Varga and drove the ball past Douglas. The Celtic defence looked bemused and fingers were pointed, but it was symptomatic of their defending.
The key strength for the Bhoys was their attack and the one-man show from Bellamy. He was immense every time he touched the ball and his running off the ball was a joy to watch.
The on-loan Newcastle striker pulled of another piece of magic in the 34th minute with an outstanding finish. Poor midfield cover from United allowed the ball to run through to the Welshman who turned on his heels and drilled a left-foot shot from 16 yards high into the net past a static Bullock.
The opening of the second period saw United in the ascendancy with Neil Lennon almost deflecting a 50th-minute strike into his own net. An excellent reaction save from Douglas prevented the equaliser.
And the keeper again was in fine form two minutes later when he dived well to clasp McIntyre's strong downward header.
With his team drifting along looking less and less likely to extend their lead, Martin O'Neill decided to change personnel and introduce Chris Sutton for the lethargic John Hartson on the hour mark.
This gave the Hoops some more impetus as they restored the balance in terms of possession. But despite this, outwith the troublesome Bellamy, there was little threat to United's goal
As it was, the Tangerines hauled themselves back into the game with a 72nd beauty from Barry Robson.
A deep ball from Grant Brebner was not cut out by Lennon, as the Irish midfielder allowed the ball to slip under his feet. McIntyre took advantage and slipped the ball to Robson, who cracked an unstoppable 20-yard shot past the keeper.
Celtic were stung into action and only a great save from Bullock two minutes later prevent Sutton from restoring their lead with a powerful low shot.
Then in the 77th minute another piece of wizardry from Bellamy saw him spin and shoot all in one movement, but it was on the wrong side of the post.
It was only fitting that Bellamy should grab the winner ten minutes from time.
The striker, who was a class apart from the other 21 players on the pitch, latched onto a flick on from Sutton and stabbed the ball low into the corner from eight yards.
O'Neill said afterwards: "His first goal was a real cracker, the second was hit brilliantly on the half-turn and his third goal was brilliant."
Celtic had to survive some scares in the final five minutes and booted the ball off the line before substitute Jason Scotland fluffed a four-yard chance.
And finally Douglas produced a magnificent save in the final minute from a Robson free-kick, O'Neill admitted he thought was "heading for the top corner".
The Tangerines had given the champions a game but it was just not enough.
Man of the Match: Craig Bellamy
The Wales international was a class above every other player on the pitch. An expert display of finishing clinched the points for Celtic and showed exactly why he will be a wanted man in the summer.