Iago Falque and Leonardo Pavoletti scored in each half in a match that had been postponed from March because of Parma's financial problems.
Parma, who have been declared bankrupt and have not paid their players all season, stayed five points adrift at the bottom with 16 points from 30 games, having had three deducted for breaching Serie A financial regulations.
Roberto Donadoni's team had staged a mini-revival, taking seven points from their previous three games, but Wednesday's defeat looks to have scuppered any hopes of an escape act.
Genoa quickly took control and Falque put them ahead when he side-footed in Marco Borriello's cross after Parma had lost possession in midfield.
Substitute Pavoletti settled the match in the 76th minute when he ran on to Diego Perotti's through pass to fire past Antonio Mirante.
Genoa's win left them seventh with 44 points, five adrift of the Europa League places.
(Writing by Brian Homewood in Berne, editing by Ed Osmond)
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