Neymar made it 2-1 with a penalty before Cavani's second just before the break effectively killed off the visitors
Paris St Germain extended their season's Ligue 1 winning streak to seven on Wednesday with a 4-1 home victory over Stade de Reims that has them already eight points clear at the top of the table.
Elsewhere Olympique de Marseille and Olympique Lyonnais kept up the probably forlorn chase with wins.
Lyon won comfortably 3-0 at Dijon, where both teams had a man red-carded, but Marseille needed a stoppage-time goal by Valere Germain to snatch a 3-2 win at Strasbourg, who had made it 2-2 a minute earlier.
Marseille had been reduced to 10 men early in the second half when Jordan Amavi was sent off for a wild tackle. In all there were six red cards in the night's seven games.
Lyon and Marseille both have 13 points from seven games, along with Lille, who lost 1-0 at Bordeaux, but PSG are away and clear on 21.
Mid-table Reims shocked the home fans in Paris when Xavier Chavalerin scored after two minutes but Edinson Cavani equalised three minutes later, superbly lobbing keeper Edouard Mendy.
Neymar made it 2-1 with a penalty before Cavani's second just before the break effectively killed off the visitors.
Thomas Meunier stretched the lead further 10 minutes after the restart and though Reims did create opportunities, PSG, with more than 70 percent possession, were always in control and Cavani missed a great chance for a hat-trick when he hit the bar in the last minute.
Bottom side Guingamp picked up their first point of the season via a goalless draw at Nimes.