Bastia defender Sebastien Squillaci was sent off for the foul which led to Ibrahimovic's 21st-minute penalty and the Sweden striker rifled in a shot from the edge of the area to double the lead just before halftime.
Ibrahimovic is banned from the Champions League quarter-final first leg against Barcelona on Wednesday due to a red card in the last round against Chelsea and is serving a four-game Ligue 1 suspension for insulting comments about a referee.
Champions PSG cruised through the second half and substitute Edinson Cavani powered in a late header before producing a clinical finish to ensure his team retained the Cup and stayed on course for a domestic treble.
They lead Ligue 1 by a point from Olympique Lyonnais with seven games left and play Ligue 2 Auxerre in the French Cup final on May 30.
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(Editing by Ed Osmond)
