But the match ended on a sour note as infighting among the Celtic players boiled over.
The gap in class between the sides was not as great as their league positions would suggest, but Celtic rarely looked threatened and Artur Boruc was untroubled for most of the match.
Celtic opened the game brightly but were quickly pegged back by Dunfermline, who were aided by gusting winds which had an impact throughout the game.
Kenny Miller had the ball in the back of the net just after the half hour mark but the referee chalked it off for offside causing anger on the Celtic bench.
Miller had the best chances of the first half but, after a bright start to the season, he has struggled to find the back of the net and East End Park proved not to be a happy hunting ground for the Scotland striker.
Aiden McGeady opened the scoring four minutes after the restart by curling the ball into the top corner of the net. Dunfermline were caught napping as Boruc blasted the ball up the pitch to McGeady.
Dunfermline have often struggled to come back once they've gone behind this season and the scenario was no different in this match as Maciej Zurawski doubled Celtic's lead 20 minutes later.
As with the first goal, the Dunfermline defence should have done better but a ball out of defence fell straight to Neil Lennon. Zurawski, with his back to goal, turned and smashed the ball past Dorus de Vries taking his tally to seven goals scored in his last three visits to East End Park.
Dunfermline snatched a consolation goal in injury time when Stephen Simmons raced in to fire in a poor clearance.
However, as the whistle went several Celtic players, including Lennon, were involved in a tussle leaving the pitch.