The striker used his strength to open the scoring at the San Paolo before Dries Mertens doubled the home side's advantage from the penalty spot
Duvan Zapata opened the scoring 19 minutes in, after out-muscling Gabriel Paletta in the area, and Dries Mertens won and converted a penalty to double the Partenopei's advantage.
Francesco Lodi struck the woodwork in the closing stages but Napoli held on quite comfortably to move into third place in the Serie A standings.
Napoli had gone into the game on the back of a disappointing defeat at the home of fellow Champions League chasers AC Milan but, despite the distraction of Monday's Supercoppa Italiana clash with Juventus in Doha, Rafael Benitez's men produced a professional performance at the San Paolo.
Indeed, the Partenopei effectively had the three points in the bag by the half-hour mark, though it has to be said, Parma proved desperately generous opponents.
For a side battling relegation, Roberto Donadoni's troops demonstrated little fighting spirit during a woeful first-half display and were fortunate not to be more than two goals down at the break.
Their defensive deficiencies were brutally exposed in the 19th minute with a poor cross from Mertens somehow managed to meet Zapata in the area. The forward's first touch was poor - but it mattered not, with the Colombia simply shrugging off Paletta's attempted challenge before firing home left-footed.
Parma gifted Napoli a second goal in the 30th minute when Massimo Gobbi stupidly barged into Mertens in the area, after the Belgium had flicked the ball over his head. Mertens picked himself up and converted from the spot - though only because Antonio Mirante failed to get a strong enough hand on the winger's weakly struck and poorly placed penalty.
Migue Britos then squandered a glorious chance to make it 3-0 after getting on the end of a free-kick in the 38th minute, but the Uruguayan centre-half headed over while completely unmarked, with Parma's defence having seemingly given up on marking altogether.
With Napoli clearly intent on conserving energy ahead of their trip to Qatar to face Juve, the second half proved both low on endeavour and excitement but Parma went agonisingly close to giving themselves a lifeline in the 73rd minute but Francesco Lodi saw his strike come back off the post.
Gonzalo Higuain, who was introduced in the closing stages, saw a goal ruled out in the dying seconds for offside but by that point Napoli had long since turned their attention to Monday's Supercoppa showdown with Juve.