Nigerian striker Victor Osimhen got his first start for Napoli, having come off the bench to lift the southerners past Parma in their opener last week.
Club-record signing Osimhen again impressed against a Genoa side playing without first-choice goalkeeper Mattia Perin, who tested positive for coronavirus, as did midfielder Lasse Schone.
Mexican forward Lozano fired Napoli ahead after ten minutes in the Stadio San Paolo with Gennaro Gattuso’s side a goal up at half time.
After the break it was one-way traffic with Piotr Zielinski latching onto a clever Osimhen back-heel flick for the second.
Zielinski then helped set up Dries Mertens for the third just before the hour mark before Lozano again struck following a mix-up in the Genoa defense. Elmas got the fifth for the hosts.
Substitute Matteo Politano curled in the sixth with 20 minutes to go to give Napoli maximum points after their first two matches.
“Last year Osimhen was the player we needed,” said Gattuso. “He didn’t score today, but he did score.
“When he attacks we find space. The players look for him, we’re very happy with how he is helping us.”
The only bad news for Gattuso was Lorenzo Insigne limping off with a left thigh injury ahead of their clash at champions Juventus next week.