Celtic's first-ever cup victory was in 1892, with Queen Victoria still incumbent as the ruling British monarch. If the Queen had been in attendance today, she would not have been amused by Celtic's performance, with the Hoops comprehensively outplayed but a very unlucky Pars side.
Dunfermline forged the first clear cut chance in the match when Jim McIntyre exploited the lack of pace inherent in Hoops centre-half Steven Pressley.
The striker slipped the ball to Mark Burchill but the former Celtic player scuffed his shot wide.
Celtic thought they had taken the lead in the 21st minute only for Kenny Clark to correctly disallow the goal for a foul on Dorus De Vries.
Celtic forged a gilt-edged chance against the run of play on the half-hour mark when Scotland striker Kenny Miller bamboozled his marker before firing a tempting cross into the box.
Dutchman Jan Venegoor of Hesselink managed to get his head to the ball but the striker's diving header flashed just wide.
The SPL champions had a glorious chance to take the lead five minutes into the second half, as an unmarked Miller got on the end of an Aiden McGeady cross, but the striker's header fell straight into the arms of De Vries.
Dunfermline were dominating possession for most of the second period and the Pars carved out a chance from nothing in the 71st minute, as a speculative ball into the box allowed McIntyre to beat Pressley to the ball but the forward's header crashed against the sidenetting.
Celtic fans rose from their seats with only ten minutes to go as Craig Beattie had a clear path of goal after skipping past marker Scott Wilson.
The supporters of the Glasgow club had to sit down in dismay as the frontman fired wide with only the keeper to beat.
Celtic eventually took the lead from the unlikeliest of sources with only five minutes left, as Jean-Joel Perrier Doumbe found himself in the box to latch on to a deflected Shunsuke Nakamura cross, stretching out a toe to deflect the ball past a bemused De Vries.
Dunfermline pressed for an equaliser but had precious few opportunities in front of goal.