Alexandre Lacazette, Lisandro Lopez, Clement Grenier and Bafetimbi Gomis scored second-half goals after Anthony Colinet was shown a straight red card seven minutes before the break.
Lyon set up a final meeting with either third division Quevilly or Stade Rennes, who will meet on Wednesday.
Ajaccio started brightly, with Mickael Colloredo hitting the post with a shot on the turn as the hosts piled the pressure.
Lyon reacted swiftly and Jimmy Briand saw off a couple of defenders in the area but his curled shot hit the bar.
Ajaccio were reduced to 10 men in the 38th minute when Colinet was sent to the dressing room for a violent tackle on Lacazette.
A brawl erupted on the pitch and the game was interrupted for almost five minutes as referee Said Ennjimi struggled to restore order and on the stroke of half-time, Kim Kallstrom's powerful free-kick smashed the bar.
Lyon, who last won the competition in 2008, eventually went ahead in the 59th minute when goalkeeper Lucas Rastello parried a fierce Briand shot into the path of Lacazette, who poked the ball into the empty net.
Lisandro doubled the tally on 73 minutes when he latched on to an Anthony Reveillere cross to put the result beyond doubt.
Clement Grenier made it 3-0 10 minutes from time with a fine chip following a poor clearance by Rastello and Gomis rubbed salt in Ajaccio's wounds with a fourth in the last minute at theend of a swift counter-attack.
The final will be played at the Stade de France on April 28.
