Second-placed Juve were held 3-3 at home by a resurgent Chievo last weekend, dropping them nine points behind leaders Inter Milan, and need a win to keep their slim hopes alive.
"It's a fundamental game for us," Gasperini told Sky TV.
"If we manage to do well against (Juve) it would be like passing the ultimate test. If it's our day, on our home turf we can manage the right result."
Genoa have lost just once at home this season but Argentine Milito, the team's top scorer with 16 league goals, looks likely to miss out with a leg injury.
Juve will be without winger Hasan Salihamidzic after he suffered a knee problem which is threatening to end his season.
Apart from bottom side Reggina hosting Udinese on Sunday, this weekend's games are on Saturday because of Easter.
All matches will hold a minute's silence before kickoff for the victims of the earthquake which struck central Italy earlier this week and the players will wear black armbands.
Serie B games due to be played on Friday have been postponed because a mass state funeral is expected to take place that day.
Roma midfielder Daniele De Rossi, whose sixth-placed side face faltering Lazio in the city derby, believes Serie A games should also have been put back, sentiments echoed by team mate Francesco Totti.
"I think right now football should be put to one side," Totti said. "We must stay close to people who now have nothing. I think it's a moment to think about other things than soccer."
Inter, still without striker Adriano as he sorts out personal problems in Brazil, host Palermo with goalkeeper Julio Cesar hoping to shake off a groin injury.
AC Milan, four above Genoa in third, visit Chievo in Verona and fifth-placed Fiorentina, two behind Gasperini's side, entertain Cagliari.
