The hosts looked to be heading for their 16th victory of the campaign after Gonzalo Higuain had put them ahead in the 18th minute.
Genoa goalkeeper Mattia Perin put in a solid performance in goal to keep the visitors in the game, however, and then Calaio snatched a point for his team with a superb free-kick six minutes from time.
The outcome saw third-placed Napoli remain six points clear of fourth-spotted Fiorentina, who were held to a 2-2 draw at Parma earlier on Monday, and extended 11th-placed Genoa's unbeaten run to three games.
Napoli went into the match on the back of Thursday's goalless result at Swansea in their Europa League last-32 first leg.
The hosts were first to threaten in the eighth minute when Dries Mertens played a one-two with Higuain before turning in the area and firing a right-footed shot that was kept out by Perin.
Higuain put Napoli ahead shortly after when he was put through on goal by an intelligent assist from Marek Hamsik, the Argentina striker beating Perin with a left-footed shot towards the far post.
Genoa almost equalised two minutes later, but Sebastian De Maio's header from Francesco Matuzalem's cross flew just over the bar.
Moussa Konate was also close to notching a leveller midway through the first half, but his goal-bound effort was cleared by Napoli defender Federico Fernandez with goalkeeper Jose Reina off his line.
Konate then tested Reina's reflexes with a powerful header which the on-loan Liverpool goalkeeper had to palm over the bar.
Napoli almost doubled their lead before half-time when Mertens got past his marker and fired a low shot towards the far post, only for Perin to make the save.
Genoa coach Gian Piero Gasperini made a surprising substitution after the interval, with Ioannis Fetfatzidis replacing the team's top scorer Alberto Gilardino.
On the hour mark, Jose Maria Callejon's close-range effort was blocked by a Genoa defender as Napoli struggled to kill the game off.
Napoli played down the clock in the latter stages of the game and were made to pay as Genoa pulled level, Calaio's free-kick stunning Reina and finding the top-right