Napoli stayed points six behind leaders Juventus, who won 2-1 at AC Milan on Saturday, with six matches each to play, and remain outsiders to win their first title since 1990 despite the win.
Higuain, who has led Napoli's challenge with 30 goals, will miss the next three games as he completes a four-match ban for his sending-off and furious reaction in last week's 3-1 defeat at Udinese.
Fiorentina's recent dismal run continued when they lost to their smaller Tuscan neighbours Empoli for the first time since 1997, leaving them fifth in the table.
Juventus have 76 points from 32 games with Napoli on 70, AS Roma on 63, Inter Milan on 58 and Fiorentina on 56.
Napoli hit the post twice and had a goal disallowed before Manolo Gabbiandini headed them in front in the 33rd minute, his fifth goal in only seven starts this season, after Verona goalkeeper Pierluigi Gollini parried Jose Callejon's shot.
The game was effectively settled in first-half stoppage time when Samuel Souprayen knocked over Callejon in the area, was sent off and Lorenzo Insigne converted the penalty.
Callejon was rewarded for his efforts when he scored the third from close-range in the 70th minute.
Fiorentina, at one stage in contention for a Champions League spot, continued in freefall as they lost 2-0 to Empoli, with Manuel Pucciarelli and Piotr Zielinski scoring late in each half for the hosts.
Paulo Sousa's team have lost four and drawn two of their last six league games.
Sampdoria pulled further clear of the relegation zone with a 2-0 win over Udinese and Torino beat Atalanta 2-1 in a midtable match.