The win sees Napoli three points behind reigning champions and current leaders Juventus with nine games remaining after former Real Madrid striker Higuain matched his career-best haul of 27 league goals in a season.
Napoli dominated their Sicilian hosts throughout but needed the award of a spot-kick on 22 minutes for Higuain to strike the decisive blow.
Walter Novellino's Palermo, meanwhile, are flirting with relegation as 18th-placed Frosinone are just one point behind them.
AS Roma remain an outside bet in the title race after beating Udinese 2-1 to register an eighth straight victory.
Luciano Spalletti has reinvigorated the Giallorossi since replacing Rudi Garcia as coach and a bright start at the Stadio Friuli produced Edin Dzeko's opening goal.
Alessandro Florenzi made the points safe in the second half, with Bruno Fernandes' late consolation providing little comfort for under-fire Udinese boss Stefano Colantuono.
Fiorentina are all but out of Scudetto contention after Eros Pisano's late leveller saw Hellas Verona snatch a 1-1 draw in Florence.
Mauro Zarate's first-half opener looked like sustaining the Tuscans' faint hopes of a first championship since 1969 but right-back Pisano punished their profligacy with a towering header on the stroke of full-time.
Chievo had a late goal disallowed for offside as AC Milan were held to a 0-0 Serie A draw that will do little to quiet speculation over Sinisa Mihajlovic's future as coach.
Mihajlovic's men travelled to the Stadio Marc'Antonio Bentegodi sixth in the table - nine points adrift of the Champions League places - and with reports indicating the Serbian could leave his role at the end of the season.
He remains hopeful of remaining in the job beyond this campaign but Mihajlovic's players did little to help his cause as they followed up last week's defeat to Sassuolo with another disappointing display.
There will also be concern over an injury to goalkeeper Gianluigi Donnarumma, who was substituted in the first half after a collision at a corner.
Milan will have felt aggrieved not to have netted the decisive goal 16 minutes from time when Ignazio Abate and Andrea Bertolacci hit the woodwork with successive shots.
Chievo then looked to have won it when Fabrizio Cacciatore - who had earlier been bloodied in his coming together with Donnaruma - saw a header into the bottom-left corner chalked off.
Veteran striker Miroslav Klose fired Lazio to a 2-0 home victory over Atalanta that kept faint dreams of European football alive.
The visitors missed two chances before half-time, with Marco D'Alessandro hitting the post before Alejandro Gomez was denied by Federico Marchetti.
In the 67th minute, 37-year-old Klose scored his first Serie A goal of the season by tapping in after Stefano Mauri's attempt had been saved, and the German was celebrating again in stoppage time as he tucked Felipe Anderson's pass away.
Lazio are 13 points shy of the nearest guaranteed Europa League berth, while Atalanta remain in 15th place.
Genoa recovered from going two goals down to pull well clear of the relegation zone with a 3-2 victory over Torino.
Ciro Immobile scored twice inside the opening 15 minutes but former Torino winger Alessio Cerci pegged his old side back with a pair of penalties.
Luca Rigoni then completed the comeback by heading Suso's free-kick beyond Daniele Padelli.
Elsewhere, substitute Jonathan de Guzman fired Carpi to a vital 2-1 victory over relegation rivals Frosinone.
The Dutch midfielder dragged the promoted side to within two points of safety with his 90th-minute penalty at the Stadio Alberto Braglia.
Carpi had taken the lead through Raffaele Bianco, but Frosinone levelled with Federico Dionisi's close-range finish.