But it wasn't the easiest of victories, despite what the score might suggest. Celtic seemed to struggle in the opening few minutes, failing to adapt to the plastic surface as quickly as they should have.
Dunfermline should have scored after only 3 minutes, when Rab Douglas was largely at fault in goal. Noel Hunt passed up the opportunity to put the Pars in front, but his header went wide.
Dunfermline did take the lead, when Celtic were temporarily reduced to ten men, as John Kennedy went off the pitch to receive treatment on an eye injury. It was Noel Hunt who scored, with a header that concerned many watching the game.
An instant reply was required, and it was Henrik Larsson who headed the equaliser on 23 minutes, from an Alan Thompson corner.
The Celtic crowd were roaring the team on to more goals, and the travelling Hoops were not let down. Once again, Alan Thompson was the provider, this time from a free-kick. Stan Varga was the man who headed home to put the Bhoys in front.
John Kennedy was replaced with Joos Valgaeren on 29 minutes.
Henrik Larsson last night proved that there is no better player in Scottish football who can rise like he does, and execute headers with such ease. The King made sure of a Celtic half time lead, minutes before half time. It was the same old story: Thompson with the assist, and Larsson with the headed goal.
Celtic could have had a couple more before half time, with Chris Sutton and the much improving Stephen Pearson coming close.
In the second half, Celtic were in easy street. Alan Thompson showed himself as a top class midfielder, and capped his man of the match winning performance with a goal. A free-kick, with the aid of a deflection added to Celtic's outstanding goalscoring record this season, and sent the Bhoys home to Glasgow with another vital three away points.
The Celtic camp were clearly not impressed with Dunfermline's plastic pitch, Martin O'Neill compared it to an ice rink, while Stephen Pearson claimed it is only a matter of time before someone is seriously injured.
The way things are going, there will be plenty more of these excuses for a playing surface in the future, but if the Bhoys can bang in 4 goals every time, I certainly won't be complaining.
Celtic:
Douglas - 6
Varga - 7
Kennedy - 6 (Valgaeren - 7)
McNamara - 6
Agathe - 6
Lennon - 8 (Lambert - 6)
Pearson - 7 (Maloney - 6)
Thompson - 9
Petrov - 7
Sutton - 8
Larsson - 9
Celtic-Mad Man of the Match: Alan Thompson