Much has been made of Cavani's often disappointing partnership with Zlatan Ibrahimovic, with coach Laurent Blanc calling for the duo to "improve their relationship" last month.
But with Ibrahimovic rested as part of seven changes made by Blanc, Cavani was given the chance to shine as the lone frontman as PSG continued their quest to win five trophies in a season.
And the former Napoli man seized the opportunity, heading in the opener in the 18th minute to set the capital club on their way to a straightforward victory.
Yohan Cabaye then made it 2-0 in the 34th minute by capitalising on an error from Nantes goalkeeper Maxime Dupe, with the visitors never threatening a comeback as PSG eased through.
The win means PSG - who won the Trophee des Champions in August - are still in contention in France's oldest competition as well as in Ligue 1, the Coupe de la Ligue and the UEFA Champions League.
PSG will attempt to boost their aspirations of defending the league title with a win over Caen on Saturday before hosting Chelsea in the Champions League last 16 next Tuesday.
It took Cavani less than 20 minutes to provide an illustration of his quality, netting with just the second chance of the game after Jean-Christophe Bahebeck had earlier drawn a save from Dupe.
Cavani was afforded too much space by the Nantes defence and duly took advantage to glance home David Luiz's free-kick.
Dupe could do little about the opener but was certainly at fault as Cabaye doubled PSG's lead.
The former Newcastle United man coolly slotted the ball into an unguarded net following Dupe's ill-advised decision to come out and punch Gregory van der Wiel's right-wing cross.
Bahebeck then went close to adding a third but Dupe did enough to keep out his low shot after the forward had worked his way down the left-hand side of the box.
Cabaye was withdrawn after half-time and replaced in midfield by Marco Verratti as Blanc sought to kill the game off, something which they achieved without pressing for a third goal.
PSG sucked the life out of the contest by at times enjoying an almost total dominance of possession, demonstrating their superiority in a manner that suggests they have what it takes to claim a significant haul of silverware.
Elsewhere, Monaco progressed with a 3-1 win over Rennes, while holders Guingamp needed extra time to beat fourth-tier Yzeure by the same scoreline.
Christophe Mandanne netted in the third minute of added time for Guingamp to force the extra 30 minutes, and then added a second before Jeremy Pied made the game safe.
