Laurent Blanc's runaway leaders moved on to 92 points with two games of the 38-match season remaining.
Uruguay forward Cavani, 29, broke the deadlock with a perfectly placed header before his clinical finish made it 2-0.
He completed his hat-trick with another header before Zlatan Ibrahimovic completed the rout in stoppage time.
The win keeps PSG 27 points clear of nearest rivals Lyon, who thrashed third-placed Monaco 6-1 and have played one game more.
Forward Alexandre Lacazette scored a hat-trick for Lyon, while former Newcastle United defender Mapou Yanga-Mbiwa got two and midfielder Rachid Ghezzal also found the net.
PSG's last two league games are away to mid-table Bordeaux on Wednesday before they host Nantes on 14 May.
Blanc's side, who have also won the French League Cup, meet Marseille in the Coupe de France final on 21 May.
Edinson Cavani scored a hat-trick as champions Paris St-Germain set a new record points total in Ligue 1 after an easy win against Ajaccio in Corsica.