Fiorentina moved level with fourth-place Inter Milan, four points behind Napoli. Verona is five points further back in sixth.
"As soon as we let our pace drop we concede a goal, we have to be more focused," Fiorentina coach Vincenzo Montella said. "Verona is a good team but we should have been more cynical, when we had a numerical superiority and were ahead by two goals.
"We have to improve on that aspect. When we were 4-2 up we had five or six chances. We have to improve, but I am happy with fourth spot."
Gonzalo Higuain scored twice for Napoli, with former Lazio striker Goran Pandev and Jose Callejon grabbing the visitors' other goals. Teenage striker Keita scored for the home side, which had leveled with an own goal by Valon Behrami.
Napoli moved six points behind leader Juventus and three behind Roma after ending a run of two successive defeats. Lazio, which remained eighth, has now not won in its past six matches and the players were loudly jeered by the home supporters at the end of the match.
"It was a fundamental match for us, we couldn't get too far off top spot," Higuain said. "I am very happy both for me and the squad.
"I scored and helped the team win. I felt the support of the fans and I've been calm even when things weren't going too well. There's still a lot of time until the end of the season, we're doing well and we have to grow."
Fiorentina took the lead in the fifth minute when Valero cut his way in from the right and fired into the bottom near corner from the edge of the area.
But the home side's advantage lasted less than a minute before Neto could only parry Iturbe's strike and the onrushing Romulo fired in the rebound.
And Hellas went in front in the 13th as Luca Toni found Iturbe, who lashed a stunning 30-yard strike into the top corner.
However, its lead also lasted mere seconds before Valero scored his second of the night, carving out space for himself just outside the area before unleashing an effort which was deflected into the top left corner.
Fiorentina restored its advantage two minutes from the break when Vargas put an angled drive into the far bottom corner.
It extended its lead nine minutes after the interval when Rossi fired a spot kick into the bottom right corner, sending the goalkeeper the wrong way.
Despite its numerical disadvantage, Verona kept pressing and got back into the game when Toni's shot was saved by Neto but Jorginho was on hand to follow up.
Verona goalkeeper Rafael pulled off a number of saves, most notably to deny Rossi, Mati Fernandez and Nenad Tomovic.
Both teams were given a standing ovation at the final whistle.
In Roma, Napoli broke the deadlock in the 24th minute with a moment of brilliance from Higuain, who ran almost half the length of pitch and held off Michael Ciani before firing under goalkeeper Federico Marchetti.
Lazio equalized almost immediately when former player Behrami, who spent three seasons at the capital club, turned into his own net.
Another Lazio old boy, Pandev, restored Napoli's lead five minutes into the second half with a swiveling shot from close range following a controversial free kick.
And Pandev, whose five years at Lazio ended bitterly after a contract dispute, sent a delightful through-ball in for Higuain to score his second in the 72nd minute.
The 18-year-old Keita reduced the deficit after a solo run three minutes from time, but Callejon sealed the match in stoppage time.
