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.

The man, from Aberdeen, was charged after "suspicious incidents" in the Aberdeen, Aberdeenshire and Montrose areas.
A report has been submitted to the procurator fiscal.
Sgt Andy Peerless, of Police Scotland, said: "The information provided to us from the public was vital."

City paid their Premier League counterparts £25m for the Ivory Coast forward two and a half years ago.
No fee has been agreed as yet and talks may continue into next week but it is anticipated Bony will return to south Wales for less than half that sum.
Bony made 46 appearances in his first 18 months as a City player, scoring 10 goals.
But 26 of those appearances were as a substitute and he was loaned to Stoke by manager Pep Guardiola last season.
Bony joined Swansea from Vitesse in 2013 and scored 25 goals in 54 games before joining City in January 2015.
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.
[NEXT_CONCEPT]
A 46-year-old man has been charged after a police appeal about someone asking women for a piggyback while they were out running.
[NEXT_CONCEPT]
Swansea City are close to securing the return of striker Wilfried Bony from Manchester City.