Two goals from Sloan Privat moved Sochaux to the brink of safety, while condemning Brest to a defeat which leaves them on the brink of relegation to Ligue 2.
Privat's second-half double subjected Brest to an eighth successive defeat which means Landry Chauvin's team are six points from safety with just two games remaining.
Following a relatively quiet opening to the match, Sochaux's Vincent Nogueira came close to opening the scoring in the 20th minute but his superb half-volley was kept out by Alexis Thebaux.
In a frantic spell midway through the first half, Brest were desperately unlucky not to take the lead.
Firstly Simon Pouplin turned away Floyd Ayite's header before, from the resulting corner, Ayite once again forced the visitors' goalkeeper into a superb save to keep the scores level.
Then, just moments later, Florian Raspentino failed to get a telling touch to Benoit Lesoimier's delivery as the hosts began to turn the screw.
Privat failed to find the target shortly before the break with an acrobatic effort, ensuring both sides went into the interval level.
Pouplin's first-half efforts paid off shortly after half-time when his side took the lead following a mix-up in the Brest defence.
Giovanni Sio crossed from the left and some hesitancy from Bernard Mendy and Thebaux allowed Privat a simple finish into an open net.
Brest thought they had levelled just a few minutes later but Florian Lejeune's header from a Mario Licka free-kick was ruled out for offside.
Sochaux's dominance continued though and Sio pounced on a Thebaux parry but saw his goalbound effort cleared away by Tripy Makonda.
The visitors continued to impress and Thebaux needed to make a magnificent save to turn Rafael Dias' free-kick on to the bar.
Sochaux's persistence paid off though when they got a second goal with less than 10 minutes left to play.
Dias swung a corner in and Privat arrived at the near post to nod the ball beyond Thebaux and secure a second successive win for Eric Hely's men.