Walter Mazzarri's side came from behind twice before reserving their best for last with two late goals earning them all three points at the Stadio Luigi Ferraris.
Ciro Immobile put Genoa in front midway through the first half, but former Genoa defender Giandomenico Mesto levelled early in the second half.
Andrea Bertolacci restored Genoa's lead almost immediately before Edinson Cavani brought Napoli level again with just over 10 minutes to go.
Napoli threw everything forward and were rewarded when Marek Hamsik put them in front for the first time in the last minute, and Insigne then completed the win with the last kick of the game.
Immobile ended his two-month goal drought in the 23rd minute to give Genoa their first lead since Del Neri replaced Luigi De Canio.
Bertolacci's shot was blocked by Paolo Cannavaro, but the ball fell to Immobile to slot in.
Ten minutes later, Immobile set up Bertolacci with a backheeled pass, but his diagonal shot was pushed onto the crossbar by Morgan De Sanctis with Bosko Jankovic sending the rebound high and wide.
Cavani wasted two chances in the final minutes of the first half, but the opening 45 minutes had belonged to the home side, who deserved their lead.
Mesto levelled for Napoli with a goal against his former club in the 54th minute, dribbling past two former team mates before scoring from a tight angle.
Parity lasted just three minutes, though, with Bertolacci putting Genoa in front once again, ghosting in unmarked at the near post to convert Luca Antonelli's cross from one yard out.
Cavani levelled for Napoli for the second time in the 79th minute when he was put through on goal by Hamsik, and he rounded Frey before slotting into the open goal.
With Napoli desperate to take all three points, and not just one, they threw caution to the wind and went in front for the first time win the last minute through Hamsik's diving header from Mesto's cross.
Insigne then completed the win deep in stoppage time, completing a counter-attack with only Frey to beat to move Napoli up to within a point of Inter and leave Genoa in the relegation zone.