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The former Real Madrid marksman opened the scoring on 24 minutes, driving into the area before dispatching a fierce effort that crept under goalkeeper Federico Marchetti.
Both goals helped spark the game to life, with Higuain seeing his bid to re-establish rebuffed by the linesman, who chalked off the Argentine's 38th-minute goal for offside.
However, the visitors legitimately edged ahead in the contest five minutes into the second half through Goran Pandev, whose left-footed effort proved too good for Marchetti.
Higuain secured his double on 72 minutes to establish daylight in the scoreline, before Keita reduced the deficit in the final minutes to set up a nervy conclusion to the encounter for Rafael Benitez's men.
Nevertheless, any hopes of a comeback were extinguished in the closing stages after Jose Callejon wrapped up the three points.
Consequently, Napoli, who remain third in Serie A, keep the pressure on the Bianconeri at the summit of Italy's top flight, with Roma sitting three points ahead of the Naples-based outfit.