First-half goals from Chris Sutton and Stilian Petrov eased them to victory and effectively took the game out of Dunfermline's reach.
Celtic again showed their menace from set-pieces with both goals coming from the training ground and, though Dunfermline threatened more after half-time, Martin O'Neill's side never looked like losing their grip.
Dunfermline threatened first and Barry Nicholson should have done better in the opening couple of minutes when he misdirected a header in front of goal.
Celtic's response was immediate with John Hartson forcing a good save from Derek Stillie, before the goalkeeper again came to Dunfermline's rescue as he blocked the Petrov's shot with his legs.
Stillie was by far the busier goalkeeper and he was at full stretch to touch a header from Sutton over his crossbar.
From the resultant corner, Alan Thompson whipped the ball in and this time Sutton produced a more exact finish with his head to give Celtic the lead after 16 minutes.
Celtic were clearly in the mood and Dunfermline were forced into some desperate defending at times.
Some careless defending by Stanislav Varga gave Scott Thomson a shooting chance for Dunfermline but his effort struck a defender and bounced wide for a corner.
Celtic went further ahead after 31 minutes when Dunfermline failed to defend a free-kick and Petrov crashed in a superb volley from 16 yards.
Stillie looked unconvincing at times as Celtic threatened at every set-piece and he struggled to deal with an effort from Bobo Balde just before half-time.
Dunfermline enjoyed their best spell in the opening minutes of the second half as they won three corner kicks in quick succession and Magnus Hedman did well to flip a header from Billy Mehmet over his crossbar.
But Hartson was desperately unlucky not to put Celtic three up moments later when he beat Stillie with a stunning shot, but the ball thumped against the underside of the crossbar.
Mehmet should have pulled a goal back at the other end when another slip by Varga put him through but he knocked the ball too far ahead of him and it allowed Hedman to close down the angle.
Dunfermline had more possession in the second half but Celtic were well organised at the back and protected Hedman well for the most part.
Hartson had the ball in the net in the 70th minute but had clearly used his hand and Hugh Dallas spotted the infringement.
Petrov created another chance for Hartson late on but this time the striker could not get enough on it to trouble Stillie.
Nicholson almost snatched a late consolation for Dunfermline but his header was well off target.