The game, postponed on Sunday because of bad weather in Brittany, quickly turned PSG's way as the visitors opened a 2-0 lead in the first 15 minutes thanks to Sweden striker Ibrahimovic and Italy midfieler Thiago Motta.
After Benoit Lesommier had reduced the arrears, Ibrahimovic, who was replaced shortly after the hour by Brazil forward Lucas, added two more before the break, including a delicate chip past goalkeeper Joan Hartock.
Argentine forward Ezequiel Lavezzi added a fifth early in the second half before Jonathan Ayite eased Brest's pain with a late consolation.
Ligue 1 leaders PSG, who fielded their top team at Brest, will next take on Montpellier at the Parc des Princes on Jan. 22.
Monaco, who qualified with a 3-2 win at third division Vannes OC last Sunday, face a trip to amateurs Monts d'Or Azergues, a fourth division side whose top player is former France and Monaco winger Ludovic Giuly.