Presnel Kimpembe was also on target for the defending champion, which remains unbeaten in 90 minutes in the competition since 2014.
The skipper headed the runaway Ligue 1 leader in front after 28 minutes at Stade de la Rabine.
Mbappe then took centre stage after the break, striking three times to put the fourth-tier side to the sword, and notching up 150 goals scored for PSG since his move there in the process.
Unbeaten against lower-league opposition in the Coupe de France since 2010, a much-changed PSG quickly imposed its authority on proceedings, enjoying more than three-quarters of the possession.
The visitors, who have won six of the last seven editions of this competition, also registered eight shots inside the opening 25 minutes, with Kimpembe, Xavi Simons, Ander Herrera and Georginio Wijnaldum all drawing saves from Clement Petrel.
But there was no denying Kimpembe, who broke the deadlock with a free header from Nuno Mendes's corner.
Kimpembe turned provider 14 minutes after the restart, Mbappe latching onto his hopeful long ball and racing away before doubling the lead.
The France striker made it 3-0 in emphatic fashion in the 71st minute as he fired a stunning 20-yard effort into the top corner from Simons's pass.
That was the talisman's fourth brace in as many appearances for PSG in all competitions.
But hungry for more, he completed his hat-trick five minutes later, playing a neat one-two with Eric Ebimbe before sliding into the empty net.