The Netherlands international scored in the closing moments to ensure Rafael Benitez's men put their Champions League disappointment quickly behind them
With the game seemingly destined to end all square, Dutchman Jonathan de Guzman ghosted into the box to turn the ball past Matia Perin from close range to secure a hard-fought win for coach Rafael Benitez.
After missing out on the chance of Champions League qualification in midweek, it took Napoli only two minutes to put the disappointment of that loss to Athletic Bilbao behind them.
Napoli attacked down the left, Lorenzo Insigne feeding Gonzalo Higain, who struck a swinging centre that met Jose Callejon arriving at the far post and his low right-footed volley beat Perin's outstretched right hand.
Genoa appeared stunned by that early strike and began to create several opportunities off crosses whipped in from both flanks.
After 19 minutes, it took a wonderful save by Rafael, down to his left, to keep out a glancing header from Chilean striker Mauricio Pinilla from Giovanni Marchese's accurate centre.
From the resulting corner on the right, Pinilla rose above everyone to flash another header just wide of Rafael's left-hand post.
The Brazilian keeper – now installed as first-choice following the departure of Pepe Reina – was in inspired form, bettering his earlier stop to again deny Pinilla who met Edenilson's lofted pass with a full-blooded header.
On the half-hour Insigne broke away on his own in a counterattack, He stopped in the box, looking for support but appeared to be felled by Stefano Sturaro, but no penalty was given.
Handed that lifeline, Genoa struck almost immediately with a well-worked equaliser. Yet again it was a cross ball which picked out Pinilla, who outjumped Kalidou Koulibaly and Camilo Zuniga to power his header high to the right of the diving Rafael.
With Benitez pacing the touchline, Napoli made the brighter start to the second period, and when Burdisso's wayward defensive header arrived at Higuain, the Argentina international controlled and turned beautifully to shoot just wide of the target.
In general, the second half missed the quality of the first 45 minutes, but Perin was forced into his first real save of the game just after the hour mark when he dived at the feet of Zuniga, while Jorginho went just too high with his shot from distance.
Substitute Dries Mertens attempted a looping first-time shot which didn't really threaten the home goal as the game entered the closing moments, and then produced a magnificent through ball for Insigne to run on to. However, with only the keeper to beat, the diminutive Italian only managed to send his shot rebounding off the advancing Perin, and a glorious opportunity to score the winner.
Then, in stoppage time, Mertens had a low diagonal shot turned wide, then watched as first Perin saved his close-range attempt before Higuain rolled the rebound straight across the face of goal.
A point apiece looked on the cards, until summer arrival De Guzman knocked home the winner, arriving late to seal maximum points for the Partenopei.