Ibrahimovic scored a brilliant first-half hat-trick to help put the tie to bed - taking his seasonal tally to 15 - with Thiago Motta also on target.
Sweden striker Ibrahimovic's goals were all different; the first an outside-of-the-boot drive, the second a back-post strike and the third a deft dink over the keeper.
Benoit Lesoimier replied for hapless Brest, before the scoring slowed down after the break with Ezequiel Lavezzi adding a fifth for the Ligue 1 leaders before another consolation from Jonathan Ayite.
PSG's next cup mission will be a trip to Montpellier.
The night's other game saw a ninth-minute goal from Samuel Gomariz earn Jura Sud Foot a 1-0 win over Creteil which brings about a next-round trip to Sete.