With his 12th and 13th goals of the season, Cavani struck each side of the interval, as did France striker Kylian Mbappe, while Julian Draxler also found the back of the net to put PSG on 32 points from 12 games.
They lead champions Monaco, who demolished En Avant Guingamp 6-0, by four points.
In the absence of Radamel Falcao, who missed the game because of a thigh injury, Guido Carrillo and Adama Traore each scored twice.
Keita Balda and Fabinho, with a penalty, added to the visitors' woes.
In Angers, PSG were a cut above despite being without the suspended Neymar, and they made sure they would not be troubled by taking a very fast start.
Mbappe drew first blood with a low, crossed shot after being set up by Dani Alves to give the visitors an early lead.
Draxler made it 2-0 nine minutes later, squeezing the ball past Mathieu Michel after collecting a perfect through ball from Alves.
Cavani put the result beyond doubt on the half hour, firing past Michel from Mbappe's clever backheel in the area for his 100th goal in 144 Ligue 1 games.
The Uruguayan scored again on the hour with a powerful shot from just inside the box following a defence-splitting pass by Javier Pastore, who was in the starting 11 for the first time in two-and-a-half months.
Mbappe rubbed salt in the hosts' wounds with a clinical finish after a pass from Lucas in the 84th.
(Reporting by Julien Pretot; Editing by Clare Fallon and Pritha Sarkar)
