The 29-year-old was high on confidence heading into Thursday's (AEDT) game after his double in the 2-1 win over Lyon on Monday, but he struggled to make much of an impact in the first half as he failed to register a single shot.
Cavani, tasked with filling the boots of the club's all-time highest goalscorer Zlatan Ibrahimovic this term, did find the net after the break, though, converting a penalty for the landmark goal after Hatem Ben Arfa was brought down inside the area by Romain Thomas.
The Uruguayan then earned a booking for removing his shirt to display the crest of Brazilian side Chapecoense, honouring those who lost their lives in a plane crash in Colombia on Wednesday.
Thiago Silva had previously opened the scoring for PSG with a fine header in the first half, just moments after denying Angers captain Cheikh N'Doye the opener with a superb goal-line clearance.
PSG's win sees is leapfrog Monaco, who drew 1-1 with Dijon on Wednesday, into second place in the table, trailing leader Nice by one point after 15 games.
The first half-chance of the game fell to Angers when Nicolas Pepe tried his luck with an ambitious long-range strike after just four minutes, goalkeeper Alphonse Areola just getting a hand out to push it wide.
PSG struggled to create any major chances of note in the opening stages, although Lucas Moura fired high and wide from a narrow angle after a good run down the right, while Ben Arfa felt he should have been awarded a penalty after a duel with N'Doye.
The visitor then came close to grabbing a surprise lead when N'Doye beat Areola with a superb header after being set up by Pablo Martinez, only for Silva to come to the rescue for PSG with an important intervention.
Unai Emery's men continued to dominate proceedings, though, and eventually got the goal it was after in the 34th minute via Silva. The Brazilian defender shrugged off his marker from Lucas' corner and beat keeper Mathieu Michel with a glancing header into the far corner.
PSG doubled its lead in the 66th minute when Cavani converted a spot-kick for his 14th Ligue 1 goal of the season. Thomas brought down Ben Arfa with a clumsy challenge inside the area and the Uruguay international made no mistake from 12 yards.
Angers made a number of attacking changes in an attempt to get back into the game, but it lacked the individual quality to trouble PSG as the host kept a clean sheet for the 10th time in its last 11 Ligue 1 games at home.
Substitute Jean-Kevin Augustin should have made it three after Ben Arfa's fine pass, but the youngster inexplicably found the side-netting after rounding the goalkeeper.
Jese Rodriguez, another player to enter in the second half, hit the upright with a low shot toward the far corner as it ended 2-0 to PSG.
Meanwhile, Nice got the job done without in-form striker Mario Balotelli with a 1-0 win over Guingamp at Stade du Roudourou.
Marseille frustrating start to the Ligue 1 season continues after it was held to a goalless draw against ASSE.