It was Lyon that kicked things off in France, and former Manchester United attacker Memphis Depay had the game's first half-chance in the ninth minute, but his strike was deflected behind.
Stefan Johansen had Fulham's first serious effort of the night, but his low strike sailed just the wrong side of the post.
Depay had another opportunity for Lyon late in the first period when he confronted Bettinelli in a one-on-one, but the Netherlands international saw his poked effort cleared at the final moment by Tim Ream.
The first chance of the second half also fell to the French outfit, with Martin Terrier hitting the bottom of the post from close range, before Aboubakar Kamara fired wide of the post down the other end of the field.
Lyon finally made the breakthrough in the 63rd minute when Mariano Diaz raced into space before squaring for Terrier, who simply could not pass up the chance to send his team 1-0 ahead.
Lyon then doubled their lead in the 74th minute when Mariano converted from the penalty spot, before Maxwel Cornet made it 3-0 four minutes later with a smart finish.
The Ligue 1 side were not finished, however, and scored a fourth in the 84th minute through Terrier as Fulham suffered a heavy defeat on the night.
LYON FIRST-HALF XI: Gorgelin, Dubois, Marcelo, Morel, Mendy, Caqueret, Ferri, Cheikh, Ndiaye, Memphis, Traore
LYON SECOND-HALF XI: Racioppi, Tete, Solet, Martins-Pereira, Rafael, Tousart, Ndombele, Aouar, Terrier, Cornet, Mariano
FULHAM: Bettinelli, Christie (S.Sessegnon 69'), Odoi (Jenz 74'), Ream (Cisse 74'), Le Marchand (Kebano 46'), Cairney (De la Torre 74'), Seri (McDonald 61'), Johansen (Thorsteinsson 74'), Kamara (Fossey 74'), Fonte (Kait 74'), R.Sessegnon (O'Riley 74')