Brest are 10 points behind leaders Paris Saint-Germain but four points clear of Lille as well as Monaco, who can go up to third if they can pick up any points in their home match against Rennes later on Sunday.
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.
