The Peruvian midfielder thumped home the winner in the 28th minute after Marco Marchionni was brought down from behind by Aly Cissokho after he had skipped past the French fullback.
The Serie A side were hungrier than their already qualified opponents and hit the post twice before taking the lead, although Lyon gave them some scares in the closing stages.
The win takes Fiorentina to the top of the group with 12 points, two more than Lyon, and makes their final game at Liverpool next month a dead match.
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"It's important for us, we've gone through," Vargas told Sky television. "We played a good match, so did Lyon, and now we hope to continue as we are."
Fiorentina were dangerous from the early stages even though Romania forward Adrian Mutu was injured and Stevan Jovetic fit enough for the bench only after a toe problem.
Mario Santana struck a post with a powerful shot in the 11th minute before Alberto Gilardino had his attempt to fire home the rebound pushed away and then hit the other post with a header from the ensuing corner.
Fiorentina sat comfortably on their lead until half-time.
Lyon's Miralem Pjanic came close with an effort from outside the box soon after the break, but the hosts continued to make more of the running.
Italy striker Gilardino dragged his shot across the face of goal from a good position before the hour mark, while Cissokho produced a fine last-ditch tackle to deny Marchionni a shot soon after.
Gilardino then volleyed wide a glorious chance created by a series of good first-touch passes.
Lyon rediscovered their attacking capabilities at the end of the match, when goalkeeper Sebastien Frey pulled off a series of stunning saves to ensure Fiorentina made it to the last 16 for the first time since the 1999/2000 season.
Vargas said his side were a different proposition this year after being eliminated in the group stage last season.
"We know each other better and we are more relaxed," he said.
