© PA Photos
The first chance of the game fell to the visitors from Naples in the third minute when Andrea Dossena shot high and wide.
Immobile broke the deadlock for Genoa in the 23rd minute when he shot home from close range.
He could have added to his tally six minutes later had Morgan De Sanctis not saved his attempt between the Napoli posts.
Napoli ended the first half the stronger of the two sides, as Cavani was first denied by Genoa goalkeeper Sebastien Frey and then failed to keep his long-range effort on target.
However, two minutes later Genoa regained their lead when Andrea Bertolacci turned in Antonelli's cross.
Insigne was unlucky not to equalise in the 75th minute when he hit the bar with a shot taken from outside the box.
Four minutes later Cavani made it 2-2 when teed up by Marek Hamsik, he made no mistake in finding the target from the left side of the box.
Hamsik himself wrapped up the points for Napoli in the final minute of normal time when he headed home Mesto's cross from close range.
Insigne added the cherry on the cake in the fourth minute of injury time with a shot from outside the box that left Frey helpless.