Ousmane Dembele scored twice and Vitinha converted a penalty to put the French champions in control in Guingamp, France, on Tuesday (Wednesday AEDT).
Having made hard work of the new-look league phase of the tournament, it would take a major upset in the second leg in Paris to deny PSG a place in the next round.
The Qatar-backed PSG are one of the wealthiest clubs in the world, but were in danger of early elimination before securing the lifeline of a playoff by finishing 15th in the 36-team league.
They weren't the only European giants facing a playoff to advance.
Defending champions Real Madrid and 2023 champions Manchester City were going head-to-head in the biggest clash of the playoffs, with the first leg at the Etihad Stadium on Tuesday.
This is the fourth year in a row they have faced each other in the Champions League, with the winner on the three previous occasions going on to lift the trophy.
City head into the first leg in the middle of a disappointing campaign that has seen their Premier League title defence unravel. But Madrid coach Carlo Ancelotti still believes his team will have to overcome one of the best in the world to advance to the round of 16.
"They are one of the best teams in Europe and they have the best manager (Pep Guardiola) out there. It's a nightmare preparing for games against him because he always has ideas that make you think," Ancelotti said.Â
"I am convinced the team that goes through from this tie will go on to win the competition."
Guardiola said he did not know what to expect from his team after a troubled season has left them in fifth place in the Premier League, 15 points behind leader Liverpool.
"We've not been consistent, when what's defined the team over the last decade has been we are an incredible machine every three days, otherwise we cannot win six Premier Leagues in seven years or win the incredible trophies we have won," he said. "Then I would feel, yes, the team is consistent, we can do it. Now it's like, I don't know."
Dembele's double saw him score for a 10th game in a row, with 18 goals during that streak.
It was his shot that led to PSG's 21st-minute penalty after Pierre Lees-Melou handled in the area. Vitinha converted the spot kick.
After Brest striker Abdallah Sima headed a corner against the post, Dembele got his first goal in the 45th minute when he broke free down the right and curled a shot inside the post.
His second came in the 66th minute when he pounced on a loose ball and burst into the penalty area to score his 23rd goal of the season.
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