The hosts, level on points with third-placed AS Roma, extended their unbeaten league run to 15 matches but could easily have secured victory having wasted other good chances.
Genoa defender Dario Dainelli, a recent arrival from Fiorentina, deflected a cross onto his own post early on and Napoli centre back Paolo Cannavaro soon unleashed a powerful shot which cannoned off the bar.
Driving rain in Naples and the continued absence of injured forward Ezequiel Lavezzi also made life difficult for Walter Mazzarri's Champions League-chasing side.
Eighth-placed Genoa had problems of their own with Napoli fans again shining lasers at the visiting players and prompting the officials to warn the home bench that the match risked being stopped.
In Saturday's other match, Bari inflicted Palermo's first Serie A defeat in eight games with a classy 4-2 home win.
Promoted Bari, whose attacking play has lit up the Italian top-flight this term, raced into a 2-0 lead inside seven minutes with Leonardo Bonucci expertly hooking in and Edgar Alvarez slotting home after the visitors gave the ball away in midfield.
Palermo, in fifth, have been in good form since Delio Rossi took over in November and they dragged themselves level thanks to Edinson Cavani's close range finish and a superb strike from Javier Pastore.
However, the Sicilians then had Fabio Liverani sent off for two bookings and seventh-placed Bari retook the lead through Paulo Barreto's penalty before Vladimir Koman sealed the win with another fine goal five minutes from time.
