The in-form Argentine got the Partenopei back on track.
Brescia were without star player Alessandro Diamanti due to suspension, while veteran goalkeeper Matteo Sereni's injury meant Michele Acari started in goal for the home side.
Meanwhile, Napoli boss Walter Mazzarri began with top-scorer Edinson Cavani on the bench opting to rest him, replaced by Jose Ernesto Sosa. Christian Maggio was also on the substitutes' bench after suffering a head injury in their last match with the Rossoneri.
There was a quick pace to the early exchanges and Lavezzi nearly took advantage of Acari's hesitation on a looping cross after ten minutes. The Argentine threatened again with a daisy cutter from 20 yards that flew just inches wide six minutes later.
After a tough challenge from Perparim Hetemaj, Hassan Yebda was left limping but able to continue. Following a corner from that incident, Andrea Caracciolo nearly opened the scoring with a powerful header.
With ten minutes remaing in the first-half a clever freekick found Caracciolo in space in the area, but the lanky striker slipped as he went to shoot and fired over the bar as the hosts began to increase the pressure on Morgan De Sanctis' goal.
The first-half ended with Napoli having dominated possession, but failing to break the deadlock in poor weather conditions at the Stadio Rigamonti.
Mazzarri eventually gave in at the outset of the second-half, throwing on Cavani for Sosa in order to find a breakthrough. However, it was the hosts that threatened next as Eder flew down the wing and crossed for Caraiccolo - his contact on the ball was awkward and although the shot wrong footed De Sanctis, it bobbled off the post and out of play.
Cavani was the next to miss when Zuniga stole the ball in the Brescia half on 65 minutes and slipped the ball into the area.
Eder then had a penalty appeal waved away by the referee after being halted by Hugo Campagnaro's challenge as he was about to pull the trigger. The defender was involved again, nearly turning the ball into his own net as his clearing header looped onto the crossbar.
Napoli got their elusive goal on 75 minutes. Hamsik had hardly been involed but set up the winner for Lavezzi. He kept close control and dribbled past an opponent before crossing and no defenders picked up the striker's run as he slammed the ball in from six yards.
Brescia boss Giuseppe Iachini's last throw of the dice was to bring on Davide Possanzini.
Goalkeeper De Sanctis was decisive late on in salvaging the result, blocking another Carraciolo attempt from a tight angle on the water-logged pitch.
With the final whistle Napoli moved into joint fourth place alongside Juventus, while Brescia suffered their fifth successive loss in the league and are back in the midst of the relegation battle and will rue missed chances.
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