Henrik Larsson cancelled out Barry Nicholson's opener for the Pars, but Dempsey was on target just over 10 minutes later, to score what turned out to be the match winner.
As the game ended, the party began, and will still be in full swing throughout the night. The players and staff were presented with the SPL trophy, for the third time in four years.
Martin O'Neill's starting line-up included the much talked about Aiden McGeady, Alan Thompson and Chris Sutton. Johan Mjallby and Jamie Smith also kept their places.
The game was always going to be an irrelevance, this thought must have also crossed the minds of the absent 14,900 Dunfermline fans who were nowhere to be seen today but will no doubt be out in force for the Scottish Cup Final later this month.
Celtic simply did not look interested in the game. Too many players were clearly looking to avoid injury, pulling out of 50/50 tackles and looking generally disinterested. Dunfermline employed the usual boring tactics of 11 men behind the ball and playing on the break.
Dunfermline scored against the run of play on 28 minutes. David Marshall produced a fine save at his near post, but the Celtic defence looked static and Barry Nicholson was left unmarked at the back post, to put the Pars 1-0 up.
McGeady showed small signs of his true potential - he is certainly one to look out for in the future. From what I am led to believe, he will soon be offered a contract, keeping him at Celtic until 2008.
In the second period, Celtic came out all guns blazing, after a lacklustre attempt to grab an equaliser before half time. Aiden McGeady's inswinging corner on 47 minutes was headed home by Henrik Larsson, and the party was back on.
But Dunfermline had other ideas, and David Marshall looked to be at fault for their second goal. Gary Dempsey's long range shot bounced up in front of the young stopper, and into the net.
Once again, Celtic attacked the Fifers, and Sutton headed off the post only a minute later. Stan Varga also came close in the scramble.
McGeady came close with a shot but it was to be his last piece of action in the game. He was substituted for Craig Beattie, when looking back, Chris Sutton should have been the one to leave the field.
Beattie looked the most promising I have seen him at Celtic. He ran at defenders, put in crosses and looked the most effective player on the park.
Rangers' friend Derek Stillie made a fantastic save to stop the match ending in a draw, pity he didn't play like that a year ago at Ibrox.
So a Dunfermline win it was, and Celtic have still failed to win a game on the new turf. The one positive thing from today was that Martin O'Neill will surely not allow a third consecutive defeat next week.
The party started, and the only thing to spoil it was the worst DJ in the world, Gerry, playing the worst singer in the world, Tricia Ferns. This woman has got to go, her versions of classic Celtic songs are a total embarrasment to the club and the great songwriters who made the songs. A complete disgrace.
Next up is the rotten mob, on Saturday, lunchtime. Hopefully the defence will be back to it's usual high standards, the absence of Jackie McNamara has been the main cause in our recent lack of victories.
Revenge, I am sure, will be sweet on the 22nd May, on Scottish Cup Final day!
Celtic:
Marshall - 7
Varga - 8
McManus - 7 (Pearson - 5)
Mjallby - 7
Lennon - 8
Lambert - 7
Smith - 4 (Miller - 6)
Thompson - 6
McGeady - 7 (Beattie - 8)
Sutton - 5
Larsson - 7
Celtic-Mad Man of the Match: Neil Lennon
Celtic-Mad Moment to Remember: The joy as the team lifted the SPL trophy.
Celtic-Mad Moment to Forget: The result.