Goalkeeper Alexis Thebaux produced a sterling performance for the home team but could not stop Swede Ibrahimovic scoring from Christophe Jallet's cross in the 55th minute.
Substitute Kevin Gameiro make it 2-0 on 73 minutes and left back Bernard Mendy's stoppage-time own goal sealed PSG's comfortable win.
PSG have 38 points, three ahead of Olympique Lyon who host fifth-placed Nice on Saturday, and Olympique Marseille, who take on St Etienne on Sunday.
"It's an ideal night. But last year we were ahead (before the winter break) and we finished second. Hopefully we'll make things turn round this time," Gameiro told beIN Sport television after scoring his fifth goal in 11 appearances.
Brest, who had midfielder Abdoulwhaid Sissoko sent off for a dangerous tackle on Ezequiel Lavezzi in the 33rd minute, are 13th on 21 points.
PSG overpowered their hosts but came across an inspired Thebaux, who made his first spectacular save after 22 minutes when he parried away Thiago Silva's header and the following Ibrahimovic shot.
Brest, who started with five defenders and a counter-attacking strategy, had their plans ruined when Sissoko was shown a straight red card. But they did protect their goal as Thebaux parried away efforts by Javier Pastore and Ibrahimovic just before the break.
The goalkeeper made another great save two minutes into the second half before Ibrahimovic broke the deadlock.
Thebaux kept his team in the match until Gameiro took advantage of slack defending to double PSG's lead and Mendy's own-goal completed the rout for the visitors.