PSG maintain perfect record under Ancelotti
Bisevac netted after only six minutes to give PSG their fourth victory in all competitions since Ancelotti took over from Antoine Kombouare during the winter break, handing Brest their first home league defeat of the season.
The win gave PSG, who are aiming to claim their first league title since 1994, 46 points from 21 matches with second-placed Montpellier on 43 after Olivier Giroud struck in the last minute in a 1-0 win at Nice.
Lille stayed third, seven points off the pace after an Eden Hazard penalty and a late double by striker Nolan Roux, who joined from Brest earlier this month, gave the French champions a 3-0 home victory against Saint-Etienne.
Olympique Lyon are fourth on 38 points after late goals by Bafetimbi Gomis and Alexandre Lacazette steered them to a 3-1 home win against Dijon.
PSG, without Argentine playmaker Javier Pastore for at least three weeks, also started without attacking midfielder Jeremy Menez, who suffered a last-minute thigh problem.
Defender Bisevac poked the ball home from a corner-kick for the winning goal. Brest suffered a blow when former French international defender Jonathan Zebina had to be replaced because of a back problem.
Although Brest dominated, PSG had a great chance to double the tally on the stroke of half-time when Mathieu Bodmer's volley smashed the crossbar.
The visitors had other opportunities after the break but neither Nene nor France striker Kevin Gameiro managed to find the back of the net.
"We knew it would be a tough game against Brest," Bisevac told French TV channel Foot Plus.
"It's a great victory, but we must keep our feet on the ground, it's a long season."