The hosts were powerless to prevent a dominant performance from the Sweden international, whose goals helped set up a round of 32 clash against Montpellier
The Ligue 1 champions had little difficulty in progressing to the competition's last 32 as the Sweden international again stole the show at the Stade Francis-Le Ble.
Ibrahimovic - who entered the match with 23 goals in 24 appearances this season for PSG - opened the scoring after only 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 the visitors' 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 pulled 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 reply was quickly quashed by two more Ibrahimovic strikes.
His second goal was a volley from six yards after poor defending, 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 Argentine producing an excellent left-footed strike from 18 yards.
The Swede 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.