The Uruguayan could even afford to miss a second half penalty as the home side dominated the game against a Lazio side who have now lost two in a row after Sunday's shock home loss to Genoa.
Napoli, who dropped their first points themselves at the weekend in a goalless draw at Catania, started nervously and could have fallen behind in the third minute when a Miroslav Klose effort was disallowed for handball.
Keen to build on that reprieve, Napoli went ahead in the 19th minute when Cavani's drilled shot from just inside the box took a deflection off Lazio defender Michael Ciani and gave goalkeeper Federico Marchetti no chance.
The home side extended their lead on the half-hour when Cavani once again drilled a shot from the edge of the box which Marchetti could get a hand to but not stop heading in the net.
In a rare chance for Lazio Stefano Mauri fired over from long-range in the 40th minute, and Napoli came close again on the stroke of half-time when Christian Maggio headed Marek Hamsik's cross over.
Lazio had a chance at the start of the second half when a cross from Abdullay Konko almost caught out home keeper Morgan De Sanctis, who managed to tip the ball over at the last moment.
Klose missed a golden chance to reduce the deficit from close-range on 54 minutes, and Lazio were made to pay 10 minutes later when Cavani rounded Marchetti in the box to complete his hat-trick.
Cavani missed his chance to claim a fourth on 76 minutes when he blazed his spot-kick over the bar after Ciani had brought down Hamsik in the box.
And Marchetti had to be alert to prevent the scoreline becoming even more embarrassing for Lazio as he saved from both Camilo Zuniga and Eduardo Vargas in injury-time.