Gonzalo Higuain's 18th-minute strike looked set to prove decisive for Rafael Benitez's side, who sit third in Serie A.
However, substitute Calaio provided a stunning twist to an entertaining match with seven minutes remaining, beating Pepe Reina with a curling free-kick from 30 yards.
Calaio was understandably restrained in celebration after his wonderful left-footed strike punished the hosts for not putting the game to bed.
Napoli now sit six points behind second-placed Roma having played a game more, while Genoa remain 11th.
After Higuain had fired wide on the turn early on, the lively Dries Mertens twice looked to find the top-right corner, narrowly missing the target with his second attempt after Mattia Perin had saved his initial effort.
The home side's early dominance was rewarded when Higuain latched on to a perfectly-weighted throughball from Marek Hamsik before lifting the ball over Perin to take his Serie A tally this season to 13 goals.
Genoa responded well, with Luca Antonelli heading over from a free-kick and Moussa Konate seeing a goalbound shot cleared by Federico Fernandez with Reina beaten.
Higuain then sent a driven strike just past Perin's right-hand post before Matuzalem escaped with just a yellow card after appearing to jump into a challenge with Fernandez.
There were further chances at either end before the interval, Mertens threatening for Napoli on two further occasions either side of Konate seeing a free header saved by Reina.
Konate dribbled into a promising position three minutes into the second half, but was unable to capitalise as Fernandez got back to make a crucial intervention.
A similarly fine challenge from Luca Antonini shut out Napoli's Jose Callejon before Genoa saw another opportunity go begging through Giuseppe Sculli, who was unable to hit the target after good work from Konate.
Sculli also brought a save from Reina with Benitez's side looking vulnerable, yet it was Calaio who had the final say.
Fiorentina twice came from behind to rescue a 2-2 draw at Parma in an ill-tempered match featuring three second-half dismissals.
Parma moved ahead through Antonio Cassano in the 39th minute, but that strike was cancelled out two minutes later by Juan Cuadrado.
An Amauri penalty restored the hosts' lead early in the second half and hopes of a second Fiorentina comeback were dented by the 53rd-minute dismissal of Modibo Diakite for a second bookable offence.
However, Vincenzo Montella's men made light of their numerical disadvantage and snatched a point courtesy of Matias Fernandez's goal with five minutes remaining.
There was still time for two further red cards as Gianni Munari and Borja Valero were sent off following an injury-time brawl.
