A tepid quarter-final affair at the Stadio San Paolo looked to be meandering towards extra-time before the former Real Madrid man showed neat reactions to divert an off-target shot past Etrit Berisha.
Despite a semi-final meeting with Roma being up for grabs, Lazio never looked like getting through, with Pepe Reina in the Napoli goal rarely tested.
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.
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 were unable to work their way back into the game and were consigned to a first defeat since Edoardo Reja's return to the capital.
