That goal was Cavani's 47th in 47 games in all competitions this season as he helped move PSG onto 83 points.
PSG were leading bottom-club Bastia 1-0 thanks to Lucas Moura's goal when controversy struck in the 35th minute.
Bastia goalkeeper Jean-Louis Leca was checking on the injured Blaise Matuidi, lying just inside the pitch by his near post; Marco Verratti, spotting the keeper out of position, fired in a shot from 20 yards that cannoned in off the crossbar to put PSG 2-0 ahead.
That means one win from their remaining three games will likely suffice for Leonardo Jardim's side to take the trophy to the Mediterranean principality for the eighth time and first in 17 years.
Bernardo Silva and Monaco have the Ligue 1 title in sight after Saturday's win.
Nancy were outclassed but could still save their season if coach Pablo Correa can guide them to victory in their next game against fellow strugglers Dijon, and get something from the visit of Saint-Etienne on the final day.
"We are each time closer to our goal but nothing is done".
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It was the ideal preparation for the Champions League semifinal return leg at Juventus on Tuesday, when Monaco will look to overturn a 2-0 deficit.
PSG midfielder Blaise Matuidi went down under a challenge and PSG claimed a penalty that was not given.
Bastia, recently punished for their home fans' inappropriate conduct against Lyon players, sat bottom with 31 points from 36 games.
However, the hosts took the throw quickly and Verratti smashed a shot into the net from the edge of the area, catching out Leca.
The defeat heaped more pressure on Bastia as they remain two points from safety, with their goal difference taking a significant hit. If anything, the goal should have been ruled out anyway, as Draxler was clearly offside and directly interfering with play by blocking Leca's view.
Lorient are involved in a relegation six-pointer against Bastia in Week 37.
PSG's Lucas celebrates after scoring against Bastia during the French League One soccer match between PSG and Bastia at the Parc des Princes stadium in Paris, France, Saturday, May 6, 2017.