Despite PSG's dominance Cavani failed to get on the scoresheet as he pursues a record 157th goal, but it wasn't for the want of trying as he failed to convert a hatful of chances.
The Uruguayan striker is on the verge of becoming PSG's all-time scorer after drawing level with Zlatan Ibrahimovic's benchmark in the 8-0 rout of Dijon last week.
Neymar left the pitch after that Ligue 1 outing angered at booing directed at him from Parc des Princes fans when he stepped up to take a penalty rather than allowing Cavani a shot at the record.
A section of the club's fans - 'Collectif Ultras Paris' (CUP) - conveyed a message of support to the Brazilian.
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"To boo our players runs contrary to our values," "Neymar PSG Cup united for Paris", home supporters wrote on banners in the stands.
Tackled about Neymar, PSG coach Unai Emery said: "He's continuing his recovery with the physio, I hope he'll be back with the team very soon.
Another high profile absentee was Kylian Mbappe, who was stretchered off after a clash with Lyon's Anthony Lopes.
"He's fine, we'll see if he can return on Saturday, but I hope he'll be ready at the latest for Lille (on February 3). It was a hard knock and the risk is getting another blow," said Emery.
Adrien Rabiot opened the scoring for PSG in the 21st minute followed smartly by Lucas Deaux's own goal, with Javier Pastore and Marquinhos completing the round of 32 win after the break.
On Cavani's record hunt Emery said: "Today he created lots of chances, but missed the final touch."
Other teams joining PSG in the next round were second division Auxerre and topflight Caen but only on penalties from lowly fifth-division outfit Canet-en-Roussillon.
On Tuesday Marseille claimed a 2-0 win at fourth-tier Epinal while Lyon were facing Monaco in Wednesday's late game.
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