The Argentine ace struck in the final 10 minutes to book a place in the last four of the Coppa Italia against Roma.
A tepid quarterfinal affair at the Stadio San Paolo looked to be meandering toward extra time before the former Real Madrid man showed neat reactions to divert an off-target shot past Etrit Berisha.
Despite a semifinal meeting with Roma being up for grabs, Lazio never looked like getting through, with Pepe Reina in the Napoli goal rarely tested.
Both sides struggled to create chances throughout much of the first half, but Gokhan Inler should have put the hosts ahead 25 minutes in. Instead, he could only scuff his six-yard effort and Lazio cleared.
Napoli took the impetus on, and Jorginho ended the first half with a curling effort from 30 yards that clipped the post on its way wide.
The second half continued in a similar vein with much of Napoli's good play coming through January signing Jorginho, although Lazio stood firm at the back and repelled their attacks well.
Former Verona playmaker Jorginho went close to snatching a win with 10 minutes of normal time to go, but his rasping drive from the edge of the area flew over the crossbar.
But Napoli grabbed a deserved spot in the last four just two minutes later as Higuain flicked in Jose Callejon's scuffed effort - the Argentinian played onside by Mickael Ciani despite visiting appeals for the flag to be raised.
A listless Lazio was unable to work its way back into the game and was consigned to a first defeat since Edoardo Reja's return to the capital, while Napoli heads on to its last four encounter with Roma.