The northerners, aiming for a first league title since 1954, recovered from a goal down to reach 55 points from 28 games.
"The pressure is now on our rivals," Lille coach Rudi Garcia was quoted as saying by French media.
Olympique Lyon looked set to leapfrog Stade Rennes into second place but the visitors snatched a late equaliser in a 1-1 draw despite being down to 10 men.
Kevin Theophile-Catherine headed Rennes level three minutes from time against the run of play after Bafetimbi Gomis had opened the scoring for Lyon by deflecting a Lisandro Lopez shot into the net in the 36th minute.
The home side looked to be cruising towards a routine win when Victor Hugo Montano was sent off in the 65th for kicking an opponent but Rennes did not give up and got their reward.
They stay second on 50 points, one ahead of third-placed Lyon, who failed to bounce back from their Champions League elimination against Real Madrid earlier this week.
Lille, still without the suspended Florent Balmont in midfield, struggled early on against Brest but their firepower was eventually too much to handle for the home side.
"With our strikers, we know we can score at any time," Lille keeper Mickael Landreau told French TV channel Foot Plus. "But I think we've played much better games this season."
Brest were rewarded with a goal for their early domination after 18 minutes courtesy of Benoit Lesoimier's angled shot.
That sparked the visitors into action and Gervinho levelled six minutes before half-time, beating goalkeeper Steeve Elana from close range after slaloming through the defence.
The Ivory Coast striker then created their second, setting up Moussa Sow in the box for the Ligue 1 top scorer to net his 19th this season with a shot on the turn in the 53rd minute.
Lowly AJ Auxerre and RC Lens kept their hopes of staying in the top flight alive with a 2-0 home win against Sochaux and a 4-1 victory at Montpellier respectively.
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