PSG stayed in command at the top of the standings with a fourth win in as many games.
Luis Enrique's team has coped with the departure of Kylian Mbappe to Real Madrid and have 16 goals so far.
Brest goalkeeper Marco Bizot managed to keep PSG at bay on Saturday until Dembele levelled the score three minutes before the interval. Romain Del Castillo put the visitors ahead from the penalty spot at the Parc des Princes.
PSG then killed any remaining suspense in the space of 80 seconds when Fabian Ruiz scored in the 73rd with a powerful strike and Dembele completed his brace in the next minute.
Despite the millions of euros invested to build a competitive team since a 2011 takeover by Qatari investors, PSG are still chasing an elusive Champions League title. They will host Girona on Wednesday in Europe's top club competition.
Brest, who also qualified for the tournament with a third-placed finish last season, play Sturm Graz on Thursday.
On a day when Marseille celebrated their 125th anniversary, new striker Neal Maupay was handed his first start by coach Roberto De Zerbi and he scored against his former club Nice
Marseille had just five shots on target and scored twice in the 2-0 win to remain unbeaten, two points behind PSG, while Nice hit the woodwork three times.
Maupay joined from Premier League club Everton on a season loan with an obligation to buy. He was trained at Nice then went on to play 160 Premier League matches with various sides.
Marseille finished the match with 10 men after centre back Derek Cornelius took too much time over a free kick and received a second yellow card.
Elsewhere, Monaco were a class above Auxerre and secured a deserved 3-0 away win with goals from Thilo Kehrer, Vanderson and Denis Zakaria.
The result moved the Principality side level on points with Marseille ahead of next week's Champions League tie with Barcelona.
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