Laup slotted the ball past Benoit Costil at the end of a sharp counter-attack three minutes into stoppage time after Karim Herouat had cancelled out Julien Feret's first-half opener for the visitors at Caen's stadium.
Quevilly, who knocked out Marseille in the previous round, will meet Olympique Lyon in the April 28 final after the seven-times French champions beat third division Ajaccio 4-0 on Tuesday.
Quevilly got off to a mediocre start but turned on the gas after the break with Rennes looking no better than a third division team.
Feret put the visitors ahead after eight minutes when he poked the ball home after a low shot had bounced off the post into his path.
Quevilly, however, hung on and started the second half brightly. They were rewarded in the 64th minute when Herouat fired a 16-metre scorcher into the top corner.
Rennes pushed hard for a winner but Jonathan Pitroipa lost the ball in Quevilly's half and on the counter attack, Laup's low, angled shot went past Costil, who sat against his post, stunned, for several minutes after the final whistle.