It was Cavani's 33rd league goal of a superb season, and his 47th in 47 games in all competitions.
The win allowed Unai Emery's side to move level on points with Monaco, although the principality side have two games in hand as well as a superior goal difference.
PSG need Monaco to slip up after a 3-1 defeat away to Nice last weekend reduced their prospects of winning a fifth consecutive title.
Matuidi looked to have picked up an injury inside Bastia's box and while goalkeeper Jean-Louis Leca went over to check on him, PSG resumed play from a throw-in and Verratti unleashed a 25-yard strike past the helpless stopper. "All the players deserve to win it".
We prefer to think that Verratti should probably have saved this wonder strike for a more opportune time and it was pretty harsh on little Bastia.
Lucas Moura and Marco Verratti were on target within the space of three minutes after the half hour, although the Italy midfielder's long-range effort arrived in controversial circumstances.More news: Pentagon: IS in Afghanistan leader killed in April raid
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Indeed, the Uruguayan demonstrated his best and worst qualities during PSG's UEFA Champions League round-of-16 match with Barcelona, scoring in each leg but also wasting several chances that would have put the tie to bed.
Bastia, recently punished for their home fans' inappropriate conduct against Lyon players, sat bottom with 31 points from 36 games.
PSG went ahead in the 32nd minute when Lucas latched on to a cross from Blaise Matuidi.
However, the hosts took the throw quickly and Verratti smashed a shot into the roof of the net from the edge of the area, catching out Leca.
Nancy are a point and a place above Bastia in 19th and there were only three points separating the basement boys and 16th-place Lorient before the day's later games got underway. 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.
Metz are safe thanks to their 2-0 win at Lille. Dijon were outclassed 4-0 at Guingamp to slide into the bottom three, replacing Caen who scored an invaluable 1-0 success at Toulouse.