An early goal from Blaise Matuidi after great work from the excellent Marco Verratti set PSG on their way, and the result never looked in doubt from then on.
After a dubious foul from Bosnian defender Emir Spahic on Ezequiel Lavezzi, Ibrahimovic converted from the spot, before adding a third soon after with the goal of the game.
From 20 yards, after the ball fell to him in space, the enigmatic Swede unleashed a half-volley, which flew into the top corner to put his side firmly in control.
In what was somewhat of a procession in the second half, Spahic saw red for a second yellow card, and the visitors could have added more, but left it until the dying moments to net a fourth, thanks to new signing Yohan Cabaye.
The result has put the tie pretty much beyond doubt, and it would take a minor miracle for the very much inferior Germans to progress from here.
Right from the word go, the Parisians were in command of this tie, and went ahead as early as the second minute thanks to a simple goal which Bayer will feel they could have done better with.
Verratti was allowed far too much time to pick his pass, laying the ball through for Matuidi, who slotted the ball under the onrushing Bernd Leno to settle any early nerves.
It was all too easy for the French champions, who passed the ball around with real ease, with Bayer reluctant to press high up the pitch.
There was a touch of fortune about PSG's second, with what seemed an innocuous challenge by Spahic on Lavezzi being adjudged to be a penalty, but Ibrahimovic converted with aplomb to put his side further in command.
However, there was no fortune about Ibrahimovic's second, firing an unstoppable strike in from the edge of the box, leaving Leno with no chance.
With the hard work done, the Parisians took their foot off the gas after the break, and another poor decision from the referee helped their cause even more.
Spahic was adjudged to have fouled Lucas Moura, who went down easily and somewhat theatrically, with the referee brandishing a seemingly harsh second yellow to the Bosnian, thus ending his participation in this tie.
Against 10 men, PSG cruised, and should have added more, with substitute Javier Pastore coming close.
But two minutes from time that fourth did come after a fine team move involving Ibrahimovic and a cool Lucas Moura lay-off, leaving Cabaye the opportunity to pick his spot, which he did with consummate ease.
The result all but ends Bayer's interest in the tournament, but sent a message to those who doubted the Parisians could replicate their league form on the continent, and are certainly in the running for glory come May.