Brest are 10 points behind leaders Paris Saint-Germain but four points clear of Lille, who lie just outside the automatic Champions League qualification spots in fourth.
“After going behind, we came back with some good football. And then there was that last quarter of an hour… but it was a good lesson to learn,” said Brest coach Eric Roy.
“We can’t relax too much, and we have to keep our wits about us right to the end. We saw the best and the worst of Brest, but in the end we won.”
Ismael Traore gave the visitors an early lead but Brest hit back with goals from Brendan Chardonnet, Kamory Doumbia and Steve Mounie giving them a 3-1 cushion at half-time.
Martin Satriano added a fourth on the hour to make a home win appear a certainty.
Metz, who are second-bottom five points from safety, hit back, however, with two goals in six minutes from Georges Mikautadze making it a nervous final 10 minutes for Brest.
PSG remained on target for the title in spite of being held to a 1-1 draw at home by struggling Clermont on Saturday.
Mindful of their Champions League meeting with Barcelona next week, PSG fielded a shadow side which needed a Goncalo Ramos equaliser with just five minutes remaining.
Monaco take third
A sole Maghnes Akliouche strike midway through the first half was enough to give Monaco home victory over Rennes, with both sides finishing the encounter reduced to 10 men.
The 22-year-old midfielder sent the Principality side third in Ligue 1 with a composed left-footed finish in the 25th minute after being teed up by Ismail Jakobs.
Rennes’ task became even more difficult immediately after the interval when forward Martin Terrier was awarded a straight red card for a foot-up tackle on Akliouche.
Steve Mandanda made a good save from Aleksandr Golovin just after the hour to keep Rennes in the tie and three minutes later, Rennes were back level numerically when Thilo Kehrer picked up a second yellow for Monaco.
With 12 minutes remaining, there was contact between Youssouf Fofana and Desire Doue in the Monaco box, but after a VAR review the referee decided there was not enough to give a penalty.
Rennes pushed hard for an equaliser in the closing exchanges, but Monaco held firm to grind out their first home win in four months.
“I’m happy to get back to winning ways at home,” said Monaco coach Adi Huetter.
Elsewhere, Montpellier put distance between themselves and the relegation play-off spot with a 2-0 win at home to Lorient.
The win takes Montpellier to 13th place and six points clear of Lorient in the play-off spot of 16th.
Nice dropped further away from the Champions League spots with a 0-0 draw at Reims and Toulouse also played out a goalless draw at home to Strasbourg.
Goals in the final 15 minutes by Alexandre Lacazette, Malick Fofana and Gift Orban gave Lyon a 3-1 win at Nantes after they fell behind to Matthis Abline’s 16th-minute opener, leaving the hosts just two points above the relegation zone.
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