After suffering their first defeat of the season in the Champions League at Arsenal on Tuesday, Napoli were quickly back on track when Goran Pandev fired them ahead after three minutes.
Dries Martens burst out of defence to slip the ball to the Macedonian who scored with an angled left-foot shot.
Switzerland midfielder Gokhan Inler added the second when his curling 30-metre shot slipped through Francesco Bardi's hands in the 26th minute and Innocent Emeghara hit the post in a rare attack for the visitors just before the break.
Jose Callejon and Marek Hamsik added further goals in the second half as Higuain's absence due to a calf muscle injury went unnoticed.
Napoli have 19 points from seven games, two behind Roma who have a perfect record after a 3-0 win at Inter Milan on Saturday.
Parma goalkeeper Antonio Mirante was dismissed in first-half stoppage time for a foul which led Domenico Berardi coverting a penalty for Sassuolo's goal.
Parma, who had gone ahead through Raffaele Palladino, still took the points when Aleandro Rosi and Cassano, who set up the other two goals, scored in a five-minute spell midway through the second half.
Sassuolo had Francesco Magnanelli sent off three minutes from time.
Catania defender Nicola Legrottaglie put through his own goal with three minutes to go to give Genoa a 1-1 draw on Gasperini's return. Previously in charge for four years at the club ending in 2010, Gasperini replaced Fabio Liverani who was fired after three games.
Elsewhere, Eder converted a stoppage time penalty to give winless Sampdoria a 2-2 draw at home to Torino and Udinese beat Cagliari 2-0.
(Reporting By Brian Homewood, editing by Justin Palmer)
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