Celtic manager Gordon Strachan claimed goal hero Jean-Joel Perrier Doumbe was one of his poorer first-half performers before hitting the late winner which clinched the double for his side.
Jan Vennegoor of Hesselink and Kenny Miller missed great chances for the Bank of Scotland Premier League champions who struggled for most of the Tennent's Scottish Cup final against Dunfermline.
The game looked to be heading for extra-time until Perrier Doumbe, the defender on loan from Rennes who was a surprise inclusion at the expense of Gary Caldwell, slid in to knock the ball past Pars keeper Dorus De Vries for an 84th-minute winner.
The right-back was playing in only his fifth game for the Parkhead side and could not have picked a better match in which to open his account in Scotland.
Strachan admitted the winner could hardly have come from a more unlikely source and said: "In the first half we had a few players below par and Joe was definitely one of them.
"He had not trained so we thought it would be beneficial for him to play.
"But the longer the second half went, those players got better, some of the them a lot better, and it made a big difference to the game."
Neil Lennon captained Celtic for the last time before leaving Glasgow for pastures new and not surprisingly the controversial character provided a talking point.
The Irishman was less than pleased when he was replaced by Gary Caldwell in the 66th minute but Strachan played down the significance of his decision
He said: "Neil has decisions to make as a captain and he knows I have tough decisions to make as a manager, but he was great about it.
"I had tough decisions choosing the substitutes but it had to be done for the game.
"Managers have tough decisions to make."
Big money signings Thomas Gravesen and Jiri Jarosik failed to even make the bench but Strachan downplayed the omission of two of Celtic's high-profile players.
He said: "Earnings have nothing to do with it. I just picked the best substitutes, plus we had the under-21 rule which restricts you."
Dunfermline manager Stephen Kenny admitted his side fell short on the day.
He said: "The club hasn't won a trophy in just under 40 years so to play as well as we did and lose was disappointing.
"I am proud of the players because everyone played well.
"You are looking for your players not to freeze, to be strong and fearless and we achieved that in the first half.
"Some of the players hadn't played recently because we had changed the team around, but that is not an excuse.
"However, we ran out of legs but we didn't run out of heart. The players put in as much effort as we could ask.
"We had to hang on in there in the second half but Celtic are not double champions for nothing.
"Overall, we can't really complain, we were beaten by a strong team."