PSG were held to a 1-1 draw by Saint-Etienne in Pochettino's first game in charge on Wednesday but had too much quality for Brest in Saturday's encounter at the Parc des Princes.
Moise Kean's 11th goal of the campaign in all competitions set the reigning champions on their way with 16 minutes played and substitutes Mauro Icardi and Pablo Sarabia each got on the scoresheet in the final 10 minutes.
The win - less emphatic than the scoreline may suggest - moved Pochettino's men within a point of pacesetters Lyon, who battled back from two goals down to draw 2-2 with Rennes and retain top spot.
Keylor Navas pulled off a theatrical save to keep out Romain Faivre's curler and PSG were in front soon after thanks to Kean, who helped the ball over the line from a yard out after Marquinhos' header hit the inside of the post and landed in his path.
Marquinhos once again came close when guiding another header on target, but Gautier Larsonneur was equal to both that attempt and Idrissa Gueye's venomous long-ranger two minutes later.
Brest are now without a win in 18 league meetings with PSG but troubled their opponents in a largely even first half, with Irvin Cardona let down by a poor first touch when clean through and Faivre seeing a free-kick pushed aside by Navas.
Larsonneur pulled off a fine save to frustrate Kylian Mbappe with an hour played and the forward curled a shot wide three minutes later as PSG - who lost Gueye to an apparent foot injury - pushed for a clinching second.
That goal arrived nine minutes from time courtesy of Icardi's composed finish following some superb play from Mbappe to get away from a pair of defenders in the opposition box.
And Icardi, making his first appearance since November after recovering from injury, teed up Sarabia to round off the scoring late on as PSG made a winning home start to Pochettino's tenure.