The third-tier side stuck gamely to the task of tackling French football's all-conquering force having made it to the Stade de France without facing Ligue 1 opposition.
Argentina midfielder Lo Celso struck the post twice before opening the scoring and, in the second half, Les Herbiers goalkeeper Matthieu Pichot came to the fore with a string of superb saves.
But Cavani forced Pichot to give away a 74th-minute penalty and he made no mistake from the spot, ensuring Unai Emery will depart Paris with a clean sweep of France's major trophies to his name.
Les Herbiers and their head coach Stephane Masala must now turn their attentions towards the far less glamourous task of ensuring their Championnat National campaign does not conclude with relegation in Friday's final round of fixtures.
11 - Edinson Cavani has scored 11 goals in 9 domestic cups finals (8 in 5 Coupe de la Ligue finals, 3 in 4 Coupe de France finals). Specialist. pic.twitter.com/Q7k2nU5k69— OptaJean (@OptaJean) May 8, 2018
Shortly after chatting with French president Emmanuel Macron during the pre-match pleasantries, Les Herbiers captain Sebastien Flochon had a 20-yard effort deflected behind for a corner inside the opening minute.
PSG smothered that adrenaline fuelled start from the underdogs and, when Kylian Mbappe's cutback was scrambled out to the edge of the box, Lo Celso struck the post left footed.
Les Herbiers' commitment to passing out of defence frequently threatened peril and Mbappe guided an eighth-minute volley against the same left upright that denied Lo Celso.
Cavani was unable to get on the end of an inviting left-wing delivery from Angel Di Maria before the Argentina international stole in unmarked a head a bouncing ball over at the back post.
Lo Celso floated a curling shot against Pichot's overworked post again but the 21-year-old midfielder finally found the corner he had been aiming for from the edge of the area in the 25th minute.
Dani Alves rippled the side netting with a superb 34th-minute free-kick and Mbappe headed wide from Thiago Silva's raking pass, but Les Herbiers avoided any further damage before the break.
A combination of Pichot and the post denied Cavani in the 49th minute following a delightful backheeled one-two from Mbappe.
The resulting corner was worked short and Mbappe thought he had PSG's second when he crashed home on the rebound, but a VAR referral showed Marquinhos used his hand from the initial attempt.
Pichot was starting to revel on the big stage, making a stunning reaction save with his left boot to deny Cavani from a Yuri Berchiche pass. A 70th-minute stop from Mbappe at point-blank range was similarly improbable.
Les Herbiers' goalkeeper belatedly blotted his night's work by taking down Cavani as the Uruguay striker looked to round him and PSG's record goalscorer put the result beyond doubt, blasting past Pichot's dive.
Roared forward by their still-buoyant supporters, Les Herbiers almost claimed a consolation goal in stoppage time but substitute Clement Couturier could not finish after rounding PSG keeper Kevin Trapp.