The part-timers, whose budget is 2,000-times smaller than the Qatari-backed Parisian giants, trailed to a goal on the half-hour by teenager Adil Aouchiche.
However, they were then awarded a penalty after Colin Dagba brought down Issa Cisse.
Up stepped Idrissa Kanoute but his tame spot-kick was well-saved by Sergio Rico in the PSG goal.
Less than a minute later, Uruguayan star Edinson Cavani, named captain for the match, tucked away PSG’s second and the game was up.
Cavani, starting a game for the first time in two months, added his second just on the hour mark before Pablo Sarabia (63rd and 70th minutes) and Eric Maxim Choupo-Moting (87th) completed the rout.
“We played seriously and with humility,” said PSG coach Thomas Tuchel.
“We deserved to win, it was a good match for the team and the club and a good start to 2020.”
Tuchel was also full of praise for Cavani who has been linked with a winter transfer window move to Atletico Madrid in Spain.
“‘Edi’ is there to score, that’s what we ask him to do. This will give him confidence, that’s the best thing.”
Andre Villas-Boas’ Marseille needed penalties to win away to fourth-tier Trelissac in their last 64 tie.
Lassana Diakhaby and Ange Gnaleko missed the crucial spot kicks for the minnows as the 10-time former winners avoided a second straight cup exit to a side from National 2.
Abdoulaye Diaby scored for the hosts after 20 seconds following a goalkeeping howler by Yohann Pele and France midfielder Dimitri Payet equalised after 20 minutes for the visitors who had Japan right-back Hiroki Sakai sent off in the closing stages of normal time.
“In your worst dreams you don’t need to suffer in that way,” Villas-Boas said.
“If we had been knocked-out without Sakai and with a humiliation like that, it would have been tough to take,” he added.
Pele made up for his early mistake by saving Diakhaby and Gnaleko’s efforts before Lucas Perrin slotted the winning penalty.
Marseille were knocked out of the competition by Andrezieux at the same stage last season.
JS Saint-Pierroise on Saturday became only the second overseas-based team to win a French Cup knockout tie and it was achieved playing more than 9,000km from home.
The club, based on the Indian Ocean island of Reunion, and which once boasted the talents of current Marseille star Payet, defeated second-division Niort 2-1.
An overseas side has only once before achieved a similar feat when Geldar FC of French Guiana made the round of 16 in the 1988-1989 season.
Saint-Pierroise’s goals were scored by Gerard Hubert and Ryan Ponti, both in the second half.
The home team’s reply also came courtesy of a visiting player when Gervais Randrianarisoa put through his own goal just after the hour mark in the game played at Niort, which sits to the north of Bordeaux.