Uruguayan forward strikes to help Walter Mazzarri's side regain momentum in race for immediate Champions League return next season
The prolific Uruguayan fired in what could prove to be two invaluable efforts to keep Walter Mazzarri's men in the race for the third and final Champions League position, after Antonio Di Natale and Giampiero Pinzi had given Udinese a clear advantage.
In a breathless match, the Cavani also missed a spot kick while Diego Fabbrini was dismissed, and in the end, both sides were happy to settle for a point apiece.
The opening goal of the encounter arrived on 28 minutes. Pinzi ghosted into the box unmarked to put away a low cross from Fabbrini, taking advantage of some less than convincing defending from the visitors in the process.
Udinese was much the better side in the first half, and minutes into the second period doubled its lead.
Giovanni Pasquale took advantage of Napoli's vulnerability with a smart cross in for Pinzi to leap unmarked and hit the post, only for the veteran Di Natale to react first and fire his shot into the ground and into the net, doubling his side's advantage.
The second half brought about a series of fiery exchanges, and eventually the tension boiled over. Fabbrini received his marching orders for persistent offenses with half an hour of the contest still to play, and from then on, Napoli took full control.
On 75 minutes it was given a lifeline following Maurizio Domizzi's reckless handball in the area, but Cavani missed the resulting spot kick, with home custodian Samir Handanovic guessing correctly to block the shot, and maintain a two-goal advantage.
But Cavani was not to be denied. Five minutes later he struck back, bending a fine 20-yard free kick which left the 'keeper rooted to the spot, and giving the visitors hope.
The visitors continued to pile the pressure on and their efforts were rewarded as Cavani brought the two sides level.
The explosive forward powered home a left-footed drive that left Handanovic helpless and sent the home crowd silent.
The result means both Napoli and Udinese remain locked on 47 points in the Serie A table, just one behind Lazio, which currently occupies third, as the race for Champions League qualification intensifies.