Burak Yilmaz’s double was not enough to make up for a three-goal deficit following headers by Ronael Pierre-Gabriel and Romain Perraud and an Irvin Cardona strike in the first half.
The result left second-placed Lille, who impressed in a 3-0 win at AC Milan in the Europa League on Thursday, on 19 points, five behind PSG who beat Stade Rennais 3-0 at home on Saturday.
Brest moved up to 13th on 12 points.
The home side opened the scoring in the 15th minute when Pierre-Gabriel headed home Perraud’s cross.
Perraud made it 2-0 four minutes later with a fine half volley as Lille struggled to cope with the hosts’ early pressure.
The Turkish striker had a golden opportunity to salvage a point for the visitors but his last-minute strike hit the crossbar.