PSG arrived under pressure after losing at home to Monaco last week, knowing another dropped result would leave them without a win from their opening four league matches for the first time since 2007.
They made the perfect start.
Joao Neves found Ousmane Dembele on the edge of the penalty area after five minutes, and the French forward picked out Torres. The Spain international needed just one touch before firing a first-time finish from around 25 yards into the bottom corner.
PSG continued to threaten as Dembele forced Brest goalkeeper Egil Selvik into a sharp save. The rebound fell to Khvicha Kvaratskhelia, but the Georgia international dragged his effort wide.
Brest, playing on an emotional night following the death of legendary manager Eric Roy, gradually found their rhythm. Pathe Mboup sent a shot over the bar before Ludovic Ajorque headed Kenny Lala's cross just wide.
PSG suffered a setback before half-time when Achraf Hakimi was forced off with an injury. Luis Enrique's side lost some of their attacking momentum as they adjusted to the change.
Selvik then denied Kvaratskhelia again as Brest continued to frustrate the European champions.
The hosts came close to an equaliser five minutes after the restart when Nuno Mendes gave the ball away near his own penalty area. Kamory Doumbia took advantage and his effort beat Matvey Safonov, only to strike the post.
PSG appeared to have doubled their advantage when Bradley Locko turned the ball into his own net, but the goal was ruled out after Warren Zaire-Emery was judged to have fouled the Brest defender.
Brest immediately threatened again. Locko picked out Doumbia, whose powerful header appeared destined for the bottom corner, but Safonov produced an excellent low save to keep PSG ahead.
The visitors were increasingly under pressure, with Willian Pacho making a crucial interception inside his own six-yard box after Zaire-Emery had been dispossessed by Mboup.
Luis Enrique responded by sending on attacking reinforcements, and the substitutes nearly produced a second goal.
Maghnes Akliouche broke down the left and delivered a dangerous ball across the area. Neves slid in to meet it, but Selvik reacted quickly to keep Brest in the contest.
Safonov was called into action again late on to deny Mboup as Brest pushed for an equaliser.
PSG ultimately survived the pressure to secure three important points and follow their midweek European victory over Slovan Bratislava with their first domestic win of the campaign.
The result gives Enrique's side some much-needed momentum ahead of next week's Le Classique against Marseille.
