The match, originally scheduled for last weekend, was delayed a second time due to heavy rains and a water-logged pitch in the weather-stricken Brittany region.
Ibrahimovic, 32, leads the domestic league scoring charts with 15 goals in 19 matches and was again in magnificent form as he opened his account on ten minutes before Brazilian Thiago Motta doubled the advantage with only 16 minutes played.
Benoit Lesoimier pulled a goal back for the second division hosts on 33 minutes before the colossal Sweden captain struck twice in three minutes to all but seal the victory before even the players headed back into the changing rooms at half-time.
Argentina international Ezequiel Lavezzi rounded out the visitors' scoring with PSG's fifth goal six minutes after the restart.
Jonathan Ayite pulled a late consolation goal back for the second division side in the final minute but by then the game was long over.
Laurent Blanc's side, who have lost just one match in all competitions this season, a league defeat at Evian, will now host Montpellier in the last 32.
"The Cup is important and its great that it continues for us, but we played well and scored a lot of goals," PSG goalkeeper Nicolas Douchez told Eurosport after getting a chance to deputise in place of first-choice goalkeeper Salvatore Sirigu.
"We were desperate to play the match after the weather problems and the delays which created a bit of a strange situation. To get to the final, you've got to beat everyone so we're looking forward to playing Montpellier in the next round at the Parc (des Princes)."
Marseille against Nice is the only other all top flight fixture in the next round to be played .