Arsene Wenger made four changes from the side that drew with Manchester United on Saturday with Olivier Giroud, Alex Iwobi, Kieran Gibbs and David Ospina coming into the side.
PSG, meanwhile, were without Serge Aurier, Angel Di Maria and Javier Pastore, but Unai Emery's side controlled the early stages and deservedly opened the scoring in the 18th minute when Blaise Matuidi rolled Shkodran Mustafi and played a ball across the goalmouth for Cavani to slide home.
Arsenal looked out of sorts and failed to respond until the 45th minute when they won what looked like a fortunate penalty with Alexis Sanchez adjudged to have been brought down by Grzegorz Krychowiak.
A scuffle followed the spot-kick decision in which Cavani appeared to strike Aaron Ramsey's chest, although the Wales international held his face but no action was taken by the referee.
From the spot, Olivier Giroud, with Arsenal's first shot of the game, confidently sent Alphonse Areola in the PSG goal the wrong way to bring Arsenal level at the break.
In the 53rd minute the visitors came close to taking the lead again when Lucas Moura struck the crossbar with a free kick after a foul by Laurent Koscielny just outside the area.
But Arsenal went in front on the hour mark, again in fortuitous circumstances, when Marquinhos' clearance hit Verratti and beat Areola from close range.
Soon after Cavani had claims for a penalty turned away after going to ground under a challenge from Koscielny.
PSG refused to give in though and fought back into the game from a Hatem Ben Arfa corner. Moura pulled away from Carl Jenkinson at the back post to direct a header towards goal which was taken away from Ospina by the head of Iwobi.
Following the equaliser, and much like in the sides' meeting in Paris earlier in the competition, Cavani squandered several chances to seal the win for PSG as they stepped up their attacking threat.
As it stands Arsenal, who travel to Basel on Dec. 6, have to better PSG's result against Ludogorets in order to win the group. In the event of both teams having the same result, the Parisiens will top Group A due to a better head-to-head record because of their two away goals.