The Ligue 1 champions had little difficulty in booking their place in the competition's last 32 as Ibrahimovic again stole the show at the Stade Francis-Le Ble.
The Sweden international - who entered the match with 23 goals in 24 appearances this season for PSG - opened the scoring after just 10 minutes, converting Maxwell's cross.
He produced a stylish finish with the outside of his right foot, giving goalkeeper Joan Hartock no chance, and Thiago Motta doubled PSG's lead five minutes later.
The goal followed a neat passing move that involved Maxwell, Ezequiel Lavezzi and Blaise Matuidi, with Motta sliding in from close range.
Brest managed to pull a goal back in the 33rd minute, as Benoit Lesoimier curled in a delightful shot into the top right corner.
The goal followed an ugly passage of play, but any hope the hosts took from that goal was quickly quashed by two more Ibrahimovic strikes.
His second goal was a volley from six yards after poor defending to convert a free-kick unmarked, before he sealed his treble with a clinical finish following a one-two with Edinson Cavani.
Ibrahimovic's influence did not stop there either, as he set up Lavezzi for PSG's fifth just one minute into the second half, with the Argentinian producing an excellent left-footed strike from 18 yards.
Ibrahimovic was taken off just after the hour-mark, as PSG sauntered to victory, but there was time for a late consolation for Brest, as Jonathan Ayite scored with one minute to play.
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