Napoli twice took the lead in the first half through Hamsik and Jose Callejon, but were pegged back by Chievo striker Alberto Paloschi on both occasions.
However, they did not look back after Hamsik helped the Partenopei re-take the lead once more and Gonzalo Higuain made sure there was no way back after bagging his first goal in Serie A following his big-money summer move from Real Madrid.
Azzurri boss Rafael Benitez warned his side they would be in for a tougher encounter at the Stadio Marc'Antonio Bentegodi than their opening league match against Bologna, over whom they eased to a 3-0 victory.
It appeared his words had an effect in the opening stages as they attacked from the off. Higuain came close after cutting in from the left and firing across goal to give Chievo goalkeeper Christian Puggioni an early save.
The visitors' fine start was rewarded in the 13th minute as they broke the deadlock in phenomenal style, with Hamsik firing into the top corner from all of 30 yards.
Yet the lead would not last long as Chievo drew level in the 24th minute with their first real sight at goal.
Finnish midfielder Perparim Hetemaj's ball into the box from the right allowed Paloschi to slot past on-loan Napoli goalkeeper Pepe Reina from close range.
Napoli re-took the lead three minutes later, however, Higuain crossing from the left by-line to leave fellow summer signing from Madrid Callejon a simple tap in.
In a frantic few minutes, the Gialloblu nearly equalised again almost immediately afterwards, with Christian Maggio's back pass intercepted by Paloschi, who could only fire against a post with his strike.
But he and Chievo would not be denied five minutes before the interval shortly after Higuain had missed the chance to double Napoli's lead with his strike going inches wide.
Then after a scramble inside the Napoli box, Cyril Thereau teed up Paloschi to fire past Reina.
Thereau himself struck over as the hosts made a decent start to the second half, while at the other end, Lorenzo Insigne went past two defenders before his curling strike to the far post from the right narrowly went wide.
Puggioni saved well from Gokhan Inler, but Napoli's persistence paid off as they re-took the lead for the third time in the match.
Inler's low cross was deflected by Chievo defender Bostjan Cesar towards his own goal and while Puggioni tremendously kept the ball out, Hamsik was on hand to score from the rebound in the 64th minute.
And Benitez's men wrapped up the win four minutes later when Higuain went through on goal and scored after Puggioni had saved his initial shot.