Florian Thauvin had levelled for the visitors on 64 minutes after two brilliantly-taken goals from Napoli’s Gokhan Inler and Higuain in as many first-half minutes had cancelled out Andre Ayew’s headed opener for the French side.
The win moved Rafael Benitez’s side into second place in the group on nine points, level with leaders Arsenal who won 1-0 at Borussia Dortmund. Marseille’s fourth straight defeat means they are strong favourites to finish bottom of the group.
“We knew this would be a difficult match before we played it. It’s a very important win because it’s an extremely difficult group,” said the match-winner Higuain, who has now scored eight goals in all competitions since signing from Real Madrid in the close-season.
The win could prove crucial for Napoli as they now travel to Dortmund for their next match in three weeks with a three-point cushion over the Germans, having beaten them 2-1 in their opening match, and only need a draw to qualify for the knock-out stages.
“Winning this match and arriving on nine points in the Champions League is positive and as a coach I have to be satisfied,” said Benitez.
“Could we have done better? Yes. But after we conceded the equaliser I really liked the reaction of the team.”
Ayew’s 10th-minute goal came as Marseille surprised nervy Napoli with swift, confident passing.
Napoli were deadly in front of goal, and equalised 12 minutes later after Federico Fernandez’s header was saved by Steve Mandanda and Swiss international Inler pounced on a poor clearance to bring down the ball with his chest and score with a looping shot.
With Marseille reeling Higuain quickly put the hosts into the lead two minutes later with a superb volleyed finish, racing onto Goran Pandev’s deflected knockdown to shoot low and hard past Mandanda.
Thauvin silenced the Napoli fans when he nipped behind a dozing Pablo Amero to substitute Dimitri Payet’s cross and volleyed past a livid Pepe Reina.
Thauvin silenced the Napoli fans when he nipped past a dozing Pablo Amero to collect substitute Dimitri Payet’s cross and volleyed past goalkeeper Pepe Reina.
Eleven minutes later, Dries Mertens sprang Marseille’s offside trap and crossed low to Higuain, who made no mistake from close range and sealed a huge victory for Napoli.
(Reporting by Terry Daley; Editing by Clare Fallon and Toby Davis)