The ball deflected in off Higuain in the 82nd minute from a Jorginho strike to send Rafael Benitez's side through to the last four with a 1-0 win where Serie A rivals Roma await.
Both sides had a handful of chances, with Brazilian Jorginho going closest before the break when his strike hit the woodwork.
However, Napoli, who are unbeaten in all competitions since the 3-1 Champions League defeat by Borussia Dortmund two months ago, found their way through the Lazio defence thanks to a huge slice of luck.
Striker Dries Mertens played the ball in only for it to be cleared, but it fell for Jorginho at the edge of the box who thumped it goal-bound. The ball appeared to be heading wide but luckily for the home side it took a deflection off Higuain and ended up in the back of the net.