Fourth-placed Fiorentina twice hit the crossbar before halftime while Napoli, who are second, were denied by a stunning double save from Ciprian Tatarusanu after the break as both sides lost ground on leaders Juventus.
Juventus, chasing a fifth successive title, have 61 points from 27 matches followed by Napoli on 58. AS Roma and Fiorentina, who meet on Friday, have 53.
The home team went ahead after six minutes when Alonso outjumped the visiting defence to head in a corner.
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Napoli's attack from the kickoff broke down but Alonso's clearance went straight to Higuain and the Argentine sent a first-time shot into the net from 25 metres, his 25th league goal of the season.
Nikola Kalinic was given a free run on goal and fired against the crossbar with only keeper Pepe Reina to beat and Cristiano Tello also curled a shot against the woodwork in another Fiorentina attack.
Tatarusanu twice thwarted Napoli in the 58th minute, parrying Jose Callejon's powerful drive after the Spaniard broke clear on the right and then brilliantly stopping Higuain's follow-up.
The Romanian also foiled Lorenzo Insigne in stoppage time, just after Higuain had a goal disallowed for offside.
(Writing by Brian Homewood; Editing by Tony Jimenez)
