Gaetano Castrovilli scored the first goal of the Serie A season as Fiorentina beat Torino 1-0 on Saturday behind closed doors before the return of a limited number of fans to stadiums 24 hours later.
Sports Minister Vincenzo Spadafora has agreed that up to 1,000 spectators will be allowed at open-air sports events in Italy from Sunday.
The Emilia-Romagna region of clubs Parma and Sassuolo have said they will open their grounds for matches against Napoli and Cagliari.
"Access will only be possible by invitation.. to invite the sponsors, who have shown great support lately," Parma said.
Nine-time reigning Serie A champions Juventus could kick off their season against Sampdoria on Sunday in Turin with fans.
In Florence, Franck Ribery wore the Fiorentina captain's armband for the first match of the new campaign.
New Torino coach Marco Giampaolo could thank goalkeeper Salvatore Sirigu for keeping his side in the game pulling off two quickfire saves on Ivorian Christian Kouame just before the break.
The breakthrough came in the 78th minute when Federico Chiesa teed up Castrovilli to beat Sirigu.
Torino captain Andrea Belotti thought he had grabbed a point deep into injury time but was ruled offside.
AS Roma open their campaign later on Saturday at Hellas Verona.