Andre Ayew had shocked the Stadio San Paolo when he headed Marseille ahead in the 10th minute from Florian Thauvin's corner, beating Napoli goalkeeper Jose Reina.
However, two goals in as many minutes put Rafael Benitez's side ahead midway through the first half and even though Marseille hit back, Argentina international Higuain was on had to net a late winner.
Gokhan Inler scored the equaliser in the 22nd minute with a left-footed volley before Higuain put the Italians in front with his second goal of the group stages.
Not to be undone and in search of their first Champions League point in this campaign, the visitors pulled level through Thauvin, who turned in Dimitri Payet's cross at full stretch from close range, but it was not enough as Higuain's second sunk Marseille's hopes.
Marseille had quickly put Napoli on the back foot through Ayew's early score which was created by a brilliantly executed set piece.
Thauvin fired in a corner and Napoli defender Christian Maggio failed to get his head on the ball ahead of the Marseille man, who nodded into the left corner with precision.
The score left the home fans shocked, and Marseille continued to look confident after their early breakthrough, with Mathieu Valbuena and Ayew both finding plenty of space.
It took a moment of brilliance from Inler to put Napoli level, the Switzerland international taking a touch on his chest before volleying the ball across goal and into the bottom right corner.
Moments later, Napoli had seized the advantage thanks to Higuain, who took the ball first time from the header of Jose Maria Callejon to beat Marseille goalkeeper Steve Mandanda.
Napoli went into half-time ahead, with both sides then struggling upon their return to the field as they lacked fluency.
Marseille went close in the 52nd minute, though, when Thauvin cut in from the right only to see his left-footed effort go wide.
The 20-year-old did find the target 12 minutes later when he poked in substitute Payet's cross, leaving Reina furious after Pablo Armero was caught on his heels.
However, the game was far from over, and Higuain claimed a vital goal for his side in the context of the group when he tapped home after Dries Mertens squared the ball to him, as Mandanda was left high and dry.
It meant Napoli moved into second place in the group thanks to Arsenal's 1-0 defeat of Borussia Dortmund.