The Ivory Coast forward volleyed home a Dimitri Payet cross on the stroke of half-time to extend Lille's unbeaten Ligue 1 run to five games. The 2011 league winners now have 20 points from 12 matches.
Saint-Etienne beat Troyes 2-0 to move up to third, level on 21 points with Valenciennes who recovered from 2-1 down to triumph 3-2 at Bastia.
Seventh-placed Toulouse were surprisingly beaten 4-2 at home by mid-table Ajaccio, missing their second opportunity in a week to go level with PSG and second-placed Olympique Marseille on 22 points.
Lille, who were hammered 6-1 by Bayern on Wednesday, dominated against Brest and took a deserved lead through Kalou in the 45th minute.
"We were expected to react and we did what we had to do," forward Payet told the Canal+ television channel.
"It was tough physically in the second half. The way we won has shown our character."
Lille almost grabbed a 12th-minute lead when Brest defender Bernard Mendy, under pressure from Kalou, went close to turning the ball into his own net.
Kalou was involved again seven minutes later, setting up Nolan Roux who failed to tap the ball in from point-blank range.
SHOT-SHY BREST
Lille struggled to maintain their grip in the second half but shot-shy Brest never posed much of a danger to keeper Mickael Landreau.
Saint-Etienne wasted a host of chances against Troyes before Renaud Cohade put them ahead on 46 minutes when he controlled the ball perfectly in the box to fire past keeper Yoann Thuram-Ulien.
Les Verts pushed hard for a second and it arrived with two minutes to go when Ligue 1's second highest scorer behind PSG striker Zlatan Ibrahimovic, Pierre-Emerick Aubameyang, collected his eighth league goal of the season.
Foued Kadir struck twice as Valenciennes beat promoted Bastia in a thriller.
Kadir opened the scoring when he beat Brazilian keeper Novaes following a quick counter-attack in the 32nd minute.
Anthony Modeste equalised from the penalty spot before Julian Palmieri put the hosts in front on 62 minutes.
Midfielder Kadir levelled for Valenciennes 16 minutes later when he bent the ball into the top corner of the net from 20 metres.
Two minutes later substitute Mathieu Dossevi ran round the back of the Bastia defence to make it 3-2.
Toulouse went ahead after four minutes against Ajaccio thanks to an own goal from Anthony Lippini.
Frederic Sammaritano quickly equalised and Chahir Belghazouani pounced on a mistake by defender Pavel Ninkov to put Ajaccio 2-1 up in the 34th minute.
Sigamary Diarra added a third goal for the visitors before Aymen Abdennour gave Toulouse hope after taking advantage of confusion in the box.
Belghazouani then sealed Ajaccio's second away win of the season in stoppage time.
