"It was more complicated than expected," said PSG midfielder Adrien Rabiot following the win over a side who had lost their previous four games in the French first division.
"We knew it would be tense and difficult because it was the semi-final of the cup and we were playing away," he added.
PSG travelled to northern France having wrapped up their fifth Ligue 1 title in six years on 15 April with a 7-1 annihilation of Monaco.
And the visitors took the lead mid way through the first-half courtesy of Mbappé who slotted home after the Caen goalkeeper Brice Samba misjudged the speed of Edinson Cavani's cross from the left.
However the hosts were level on the cusp of half-time via a series of ricochets. A deflected shot fell to Ismael Diomande and his strike towards the goal bounced off Adrien Rabiot to leave the PSG goalkeeper Kevin Trapp stranded.
With the tie heading towards extra-time, Mbappé added his second.
But before the goal was confirmed, the video assistant referee was consulted to see whether Cavani was offside when he ran on to a slick backheel by Angel Di Maria before he set up Mbappé.
Once the France international's strike was verified, Caen went looking for a late equaliser and were caught on the break in stoppage time.
The victory furnishes PSG with the chance to claim an unprecendented fourth consecutive cup triumph and extend their own record of overall wins to 12.
"The final will be a great match," added Rabiot. "Les Herbiers will bring their weapons and so will we. Even though they are in the third division, we will take the final seriously. We've seen what can happen in this competition so I'm sure the coach will prepare us properly for the game."