The defending champions had entered the fixture without a league win after their first three matches, making the narrow victory an important result for Luis Enrique's side.
• Brest: No goals
• Paris Saint-Germain: Ferran Torres 5'
PSG made the perfect start when Torres opened the scoring in the fifth minute. The Spanish forward finished a swift attacking move involving João Neves and Ousmane Dembélé, sending a low effort beyond Brest goalkeeper Egil Selvik.
The goal continued Torres' outstanding start to life in Paris. It was his sixth goal in five appearances for PSG, following his impressive goalscoring form since joining the French champions.
PSG had opportunities to extend their advantage, with Khvicha Kvaratskhelia among the visitors' main attacking threats. However, the champions were unable to turn their early dominance into a second goal.
Brest gradually grew into the contest and began causing PSG problems. Kamory Doumbia struck the post after the interval, while Ludovic Ajorque also tested the visitors' defence.
PSG were dealt another setback when Achraf Hakimi was forced off with a muscle problem before half-time, with Fabián Ruiz introduced in his place.
The home side continued to push for an equaliser in the closing stages, but PSG goalkeeper Matvey Safonov produced several important saves to preserve his team's lead.
Safonov was particularly important late on when he denied Pathé Mboup from close range, helping PSG withstand Brest's final pressure and secure all three points.
The result lifts PSG to five points from four Ligue 1 matches, after two draws, one defeat and Sunday's victory. Brest, meanwhile, suffered their first league defeat of the campaign after beginning the season unbeaten.
For PSG, the victory provides some relief after an unusually slow start to their title defence. Their European form had already offered encouragement, with a 6-1 Champions League victory over Slovan Bratislava, and Torres' continued goalscoring form is another major positive for Enrique.
PSG will now turn their attention to a major Ligue 1 test against Marseille on 20 September, while Brest travel to face Auxerre.