Neymar and Kylian Mbappe headlined a strong PSG side, but they needed a Sylvain Jule own goal to break the deadlock.
Making his 50th PSG appearance, Neymar hit the woodwork in the first half and eventually scored with 20 minutes remaining.
Mbappe added further gloss from the penalty spot soon after, with Julian Draxler getting in on the act as the 12-time winners took their first step towards a fifth-successive Coupe de France triumph.
Clement Daoudou pulled off fine saves to deny Dani Alves and Kylian Mbappe early on, but he was powerless to prevent PSG's 24th-minute opener.
Jule was well placed to cut out Neymar's cross, only to panic when the ball came to him and send his attempted clearance looping in over Daoudou.
Florian Jegu snatched at a chance to promptly restore parity and that profligacy almost proved costly when Neymar's deflected free-kick hit the upright.
Neymar took matters into his own hands as the hour approached, but Daoudou was alert to the Brazilian's clever chip.
Daoudou was at his best again soon after to tip Draxler's attempt over, but was finally beaten for a second time when Neymar drilled in from close range.
The floodgates were open and, after Mbappe sent Daoudou the wrong way from 12 yards following a clumsy foul from Florian Paillot, Draxler chipped in a fourth to round off the rout.
What does it mean? Tuchel takes no chances
With a Coupe de la Ligue quarter-final against Guingamp coming up, it would have been easy for Thomas Tuchel to rest PSG's star names, but instead he showed just what the competition means to the Ligue 1 leaders by selecting the likes of Neymar, Mbappe and Thiago Silva.
While the selection ensured that PSG had the quality to breakdown their determined opposition and avoid the fate suffered by Marseille earlier on Sunday, it also gave Pontivy's players the chance to go up against some of the world's finest.
Daoudou takes his chance to shine
Pontivy's goalkeeper was always likely to be busy, but despite conceding four times, the 24-year-old did himself proud with a series of superb stops, and his performance could well attract some bigger clubs.
Own goal spoils Jule's big day
Jule put in a bright display in midfield as the youngster looked to impress against France's best side, but his performance will unfortunately be remembered for the dreadful own goal which put PSG ahead.
PSG's focus now switches to Guingamp on Wednesday, before they travel to Amiens in their first Ligue 1 fixture of 2019.