Napoli wore shirts adorned with commemorative patches to honour Hamsik scoring his 116th goal for the club against Sampdoria last weekend – surpassing Diego Maradona's long-standing record.
The Slovakia midfielder continued a current purple patch to score his third in as many matches with an assured finish after 17 minutes, extending the advantage over Juventus for Maurizio Sarri's men at the summit to four points ahead of the weekend action.
Hamsik had number 117 in his sights after 10 minutes when he exchanged passes with Lorenzo Insigne but saw his effort deflected behind by Stefan Simic.
It arrived soon enough when, following another one-two – this time with Allan – Hamsik broke into the Crotone box and drilled an unerring low shot beyond Alex Cordaz.
It was a swashbuckling display at times from the Serie A leaders, who were denied a second when Cordaz extended himself to tip over when a brilliant dummy from Jose Callejon set up Insigne.
Crotone, who will see in the new year in the relegation zone, improved after the break and a sloppy clearance from Napoli goalkeeper Pepe Reina almost allowed Marcello Trotta to equalise from out on the right flank.
Reina's opposite number Cordaz was busy excelling himself, getting a vital touch to a curing Insigne strike from 25 yards that came back off the bar
A magnificent double save from substitute Amadou Diawara's long-ranger and Callejon on the follow-up concluded a fine night's work from Cordaz.
Napoli take the informal title of campioni d'inverno or winter champions, with victory ensuring they are leaders at the halfway stage of Serie A. Two seasons ago, Napoli became the only side over the past decade to earn this distinction and not claim the title in May.
