PSG was held to a 1-1 draw by Saint-Etienne in Pochettino's first game in charge on Thursday (AEDT) but had too much quality for Brest in Sunday's (AEDT) encounter at Parc des Princes.
Moise Kean's 11th goal of the campaign in all competitions set the reigning champion on its 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 pacesetter Lyon, which 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 was in front soon after thanks to Kean, who helped the ball over the line from a yard out after Marquinhos's 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 is now without a win in 18 league meetings with PSG but troubled its opponent 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, which lost Gueye to an apparent foot injury, pushed for a second.
That goal arrived nine minutes from time courtesy of Icardi's composed finish after some superb play from Mbappe to get away from a pair of defenders in the opposition box.
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.