The result, secured after Gianluigi Donnarumma saved a late penalty from Islam Slimani, means Christophe Galtier's side have 19 points from seven games, two more than second-place Lens, who led the table after a 1-0 win over Troyes on Friday.
Brest came into the contest having conceded a club-record 16 goals in their first six games and were carved open in the 30th minute despite a bright start as Neymar fired in from a tight angle after being played through by Lionel Messi.
The visitors were lucky not to be reduced to 10 men minutes earlier. Christophe Herelle was shown a red card for scything down Neymar, but a review prompted the referee to reverse his decision as the PSG forward was offside before the tackle.
The hosts turned the screw on their opponents and both Messi and Kylian Mbappe squandered clear opportunities either side of halftime before 17th-placed Brest were awarded a spot kick but Slimani's tame 70th minute effort was kept out by Donnarumma.
"It was very difficult. It was important to win after the Champions League and we did that," Donnarumma said, referring to last week's 2-1 win over Juventus.
"We're also happy for our fans who are always there for us and we wanted to win for them. It's really important to be able to suffer together and we saw that today."
Presnel Kimpembe, whose challenge on Noah Fadiga led to the penalty, went off injured late on to leave PSG with 10 men after they had used up their substitutes but experienced defenders Sergio Ramos and Marquinhos helped them see out the match.
Donnarumma was instrumental in ensuring the home side got the win as he was called into action again with a diving save after the ball appeared to be going in at the near post off Slimani's shoulder following a whipped cross from the left.
"It was a game with two completely different halves," said Galtier. "A first half in which we created a lot of chances and deservedly scored the opener.
"We could have and should have scored more but didn't and that's why I decided to stay with the attacking trio, to cause problems and have a big lead at halftime and be able to have better game management.
"It wasn't the case and it was much tougher in the second half ... we made technical mistakes up front, in midfield and at the back. That gave Brest a lot of hope ... when the opponents are only one goal behind in Paris, they're going to believe."
The victory extended PSG's winning run against Brest to 12 games but it was far from comfortable and they will aim to iron out issues in attack before Wednesday's Champions League game at Maccabi Haifa and next Sunday's trip to Olympique Lyonnais.