Catania thrashed Palermo 4-0 in the clash of the two Sicilian teams while Alessandro Matri continued his impressive form for Juventus, scoring his sixth goal since joining them at the end of January in the 2-0 win at AS Roma.
Napoli stayed three points behind leaders AC Milan, who have 65 points from 31 games after Saturday's 3-0 win over Inter, and moved above the defending champions.
Uruguay striker Cavani took his Serie A tally to 25 goals, level with Udinese's Antonio de Natale, as Napoli kept alive their scudetto hopes in a fiery match which left the visitors fuming at three key decisions.
Lazio appeared to have a goal wrongly disallowed with the score at 2-2 when Cristian Brocchi's long-range effort bounced down off the crossbar. Replays suggested it had crossed the line by at least a metre.
"You can see very well, it wasn't a case of five centimetres over the line, it was very evident that it went in, there's no way you can consider that it was not a goal," said Lazio president Claudio Lotito.
The visitors, who stayed fifth in the table two points behind Udinese in the Champions League qualifying round spot, were also angry with the Napoli penalty which made it 3-3 and said Napoli's winner came from an offside position.
Stefano Mauri put Lazio ahead with a delightful individual goal, weaving his way past several defenders and scoring with the subtlest of touches as he flicked the ball past the helpless Fernando Muslera into the far corner in the 29th minute.
Minutes later, he nearly scored again from an identical position but this time sent his effort past the post.
It did not seem to matter when Brazilian defender Andre Dias doubled Lazio's lead in the 57th minute, sticking out his foot to volley in from Javier Garrido's whipped free-kick.
However, Napoli were level within five minutes with goals from Andrea Dossena and Cavani, both following free-kicks which Lazio failed to clear.
That was followed by the Brocchi incident, Lazio's protests barely subsiding before they were gifted the lead when Salvatore Aronica turned the ball into his own goal from close range.
UGLY EXCHANGE
The hosts levelled again when Giuseppe Biava and Cavani both fell in the penalty area, the referee awarding a penalty and sending off the Lazio player before Cavani converted in the 82nd minute.
With two minutes left, Cavani broke clear of the Lazio defence and cleverly lobbed over his compatriot Muslera who got a hand to the ball but could not stop it going in.
Cavani and Giuseppe Sculli were booked for an ugly exchange which led to a mini-brawl in stoppage-time and the Uruguayan was lucky not to be sent off for diving seconds later. "We were born to suffer," said Napoli coach Walter Mazzarri.
"At one point it seemed that we were jinxed, but we managed to turn things around.
"We complicate life and we need to improve from this point of view but with football, determ
