Lisandro gave his side the lead in the 28th minute with a clinical finish, before both sides hit the woodwork in a frenetic second half with Quevilly midfielder Anthony Laup coming agonisingly close to restoring parity.
Quevilly, who are currently struggling in the lower half of France's third tier, battled furiously in the second half, but Regis Brouard’s men could not muster an improbable equaliser as Lyon claimed a valuable piece of silverware.
Lyon’s Brazilian duo missed the match: Ederson had a hamstring problem, while Bastos was suffering from back pain, but Yoann Gourcuff was handed a start after returning from ongoing fitness problems.
Quevilly entered their first Cup final for 85 years with no major injuries to report. Goalkeeper Issa Coulibaly was confined to the bench as Yassine El-Kharroubi got the nod, while top scorers Julien Valero and Pierrick Cappelle led the line.
The amateur side started very brightly and won a corner early on with Hugo Lloris having to fly out and rather unconvincingly claim a high ball under pressure.
Lyon enjoyed a good spell of pressure and, in the seventh minute, Lisandro almost stole in at the back post to convert a deep cross from Alexandre Lacazette, but he could not quite turn the ball in from an acute angle.
The Lyon forward went even closer in the 12 minute as he took a high ball down into his stride with an exquisite touch, before unleashing a fierce shot which cannoned off the near post.
Quevilly had fleeting forays into their opponent’s half, however, and Matthias Jouan was allowed too much space to run with the ball before he fired a stunning drive which zipped agonisingly over the crossbar.
Lyon had to make an enforced change in the 19th minute as Babary Kone came on to replace the injury-stricken Dejan Lovren, and their pressure continued to be incessant thereafter.
Frederic Weis made a stunning clearance off the line four minutes later as Maxime Gonalons fired a low shot on target with Quevilly goalkeeper Yassine El Kharroubi out of position.
Finally Lyon’s dominance paid just before the half hour mark: El Kharroubi flew out of his goal recklessly and proceeded to pull out of a challenge with Bafetimbi Gomis, with Lisandro on hand to promptly fire the ball into the empty net.
Yoann Gourcuff caused havoc in the final third throughout, but scuffed his shot in front of goal as the ball broke loose to him after fine work from Lisandro outwide on the left just before half-time.
Lyon came agonisingly close to doubling their lead six minutes after the restart as the ebullient Lacazette hit the woodwork as his shot from 25 yards took a vicious deflection and cannoned off the underside of the crossbar with El Kharroubi comprehensively beaten.
But Quevilly never looked out of the match, and a searing break from Laup saw the midfielder hurtle through on goal, only for his fierce left-footed shot to be brilliantly tipped onto the crossbar by Lloris.
Further chances followed, with Gomis dragging a very poor effort wide of the far post with the goal gaping at his mercy after fine work from Kim Kallstrom out on the left flank.
Minutes later, substitute Jimmy Briand flew through on goal with just El Kharroubi to beat, but the Quevilly goalkeeper did superbly to make himself big and save with his feet.
The scoreline did not change late on as Lyon preserved their slender advantage, albeit in rather unconvincing fashion at times, and the Ligue 1 side prevailed in front of their jubilant supporters.
Quevilly were the third club from the third level of French football to reach the final of the Coupe de France - after Nimes in 1996 and Amiens in 2001 – and they gave a fine account of themselves, albeit with Lisandro and Lyon left to celebrate a precious piece of silverware.