Less than 48 hours ahead of the Stade de France showpiece, Ibrahimovic - who passed 100 goals for the club with a hat-trick in midweek against Saint-Etienne - was given a ban for comments made after PSG's 3-2 Ligue 1 loss to Bordeaux.
With the fourth game of his ban suspended, that sanction will see him miss Ligue 1 games with Nice, Lille and Metz, but he bounced back in the ideal manner with a brace to deliver PSG their first major trophy of the season.
The holders were given a huge helping hand as Bastia centre-back Sebastien Squillaci was sent off for bringing down Ezequiel Lavezzi, with Ibrahimovic lashing home the resulting penalty.
Although the dismissal ruined the contest as a spectacle, it was welcome relief to a PSG side set to face Barcelona in the UEFA Champions League on Wednesday - their coach Laurent Blanc having recently complained about fixture congestion.
Bastia were powerless to prevent Ibrahimovic from taking advantage of the extra man and ending the encounter as a contest, with substitute Edinson Cavani scoring twice late on to seal the the maiden trophy of a prospective quadruple.
PSG created little in the opening stages but were presented with a gift in the 19th minute when Squillaci tripped Lavezzi, leaving referee Benoit Bastien with little choice to point to the spot and brandish a straight red card.
And Ibrahimovic, who had laid the ball off for Lavezzi in the build-up, made no mistake as he emphatically slammed the ball past PSG loanee Alphonse Areola from 12 yards.
The capital club unsurprisingly controlled proceedings with their numerical advantage, and Ibrahimovic capitalised in the 41st minute to effectively put the game beyond doubt.
Ibrahimovic powered a precise low finish into the bottom-left corner from just outside the box after Bastia had failed to fully clear Serge Aurier's right-wing cross.
Only a strong one-on-one save from Areola prevented PSG from making it 3-0 through Lavezzi, who then rolled an effort narrowly wide of the right-hand post less than 90 seconds after the restart.
Bastia named striker Brandao on the bench eight months after his infamous headbutt on PSG midfielder Thiago Motta after their league clash in August, which saw him receive a six-month ban.
Squillaci's red defeated the object of the Brazilian's presence - although he did come on in the closing stages - but the Corsicans went close to pulling a goal back, Florian Marange heading wide from Ryad Boudebouz's free-kick.
Areola thwarted Marco Verratti and Marquinhos either side of Lucas Moura's return for the Trophee des Champions winners after two months out with a groin injury.
Thiago Silva cleared a Floyd Ayite effort off the line, before Cavani steered in a third 10 minutes from another Aurier delivery and slotted in his second in stoppage time to put the gloss on a successful cup defence.
