The first chance of the match fell to Goran Pandev, whose left-footed shot from close range from a Cavani cross went wide.
Seven minutes later, Michael Ciani tried an ambitious shot from over 35 yards but failed to keep it on target.
Napoli went ahead in the 19th minute when Cavani shot home Marek Hamsik's pass from outside the Lazio penalty box.
Hernanes could have restored parity for the visitors in the 28th minute had his shot from outside the box not been saved by Morgan De Sanctis.
Three minutes later, Cavani made it 2-0 to Napoli with a right-footed shot from the right side of the box after being sent through by Paolo Cannavaro.
Christian Maggio almost scored the hosts' third goal of the evening on the stroke of half-time when his header from a Marek Hamsik cross went over the Lazio crossbar.
Cavani completed his hat-trick in the 64th minute as he found the target from close range after being sent through by Hugo Campagnaro.
The Uruguayan striker had a great chance to add another goal to his tally on 75 minutes when Napoli were awarded a penalty.
Ciani's foul on Lorenzo Insigne inside the area saw the referee point to the spot, but Cavani failed to convert the penalty.
Napoli created a number of chances thereafter, but failed to add to their tally.