The victory took Napoli back to the top of the table with 15 points from their first five league games under Spalletti
Victor Osimhen scored twice as Napoli crushed Sampdoria, 4-0, Thursday to remain perfect in Serie A and return to the top of the table.
In the other early game Ciro Immobile converted an added-time penalty to give Lazio a 1-1 draw at Torino.
In the late game, Tammy Abraham scored his first home Serie A goal to give Jose Mourinho's Roma a 1-0 victory over Udinese.
In Genoa, visiting Napoli rode their luck in the first 35 minutes.
After 11 minutes home goalkeeper Emil Audero was fooled when Osimhen mishit a close range volley and had already fallen back across the goal line by the time the softly-struck ball floated into his grasp.
Sampdoria responded by besieging the Napoli goal, but David Ospina foiled a series of incisive attacks with a string of acrobatic saves.
Napoli took control after 39 minutes when Fabian Ruiz passed the ball into the corner of Audero's goal from 20 meters.
Osimhen added a second after 50 minutes, running onto Hirving Lozano's low cross from the right and drilling the ball home from the edge of the six-yard box.
Last season, his first with Napoli, the Nigerian missed more than two months after injuring a shoulder on international duty and then catching Covid-19 while recuperating.
Piotr Zielinski added a carbon copy goal nine minutes later as he met a low Lozano pullback with a crisp shot.
Osimhen could have had more.
He had a strike late in the first half ruled out for offside and later dragged his shot wide when one-on-one with Audero.
The victory took Napoli back to the top of the table with 15 points from their first five league games under Luciano Spalletti.
They moved two ahead of champions Inter Milan, who won 3-1 at Fiorentina Tuesday, and AC Milan, who beat Venezia Wednesday.
Sampdoria dropped to 13th, slipping behind Juventus on goal difference.
Roma climbed to fourth, another point back, after edging out Udinese with Abraham scoring the only goal.
Teenage right back Riccardo Calafiori battled up the wing and into the penalty area in the 36th minute.
His hard low cross beat Marco Silvestri's dive at the near post but forced Abraham to quickly adjust his feet, turning his back to goal and guiding the ball into the unguarded net with the heel of his right boot as he fell over.
Roma finished the game with 10 men after skipper Lorenzo Pellegrini was shown a second yellow card in the 90th minute.
In Turin, penalty specialist Immobile snatched a point for Lazio with a 91st-minute spot kick.
Marko Pjaca gave Torino the lead in the 76th minute with a crisp header.
As the game entered added time, Koffi Djidji caught Vedat Muriqi with a clumsy challenge.
Immobile rolled in the penalty for his league-leading sixth goal of the season to secure a draw.
Immobile said he felt Lazio should not have needed his late penalty.
Sampdoria 0 Napoli 4 (Osimhen 10, 50, Fabian 39, Zielinski 59)
Torino 1 (Pjaca 76) Lazio 1 (Immobile 91-P)
Roma 1 (Abraham 36) Udinese 0