Rafael Benitez's side headed to the Stadio Armando Picchi with a chance to cut the gap to Roma, placed second in Serie A, to four points following the capital club's goalless draw with Inter 24 hours earlier.
And Napoli looked to be on their way to victory when Dries Mertens put them ahead with a 32nd-minute penalty.
But the visitors' lead lasted only seven minutes as Domenico Di Carlo's belagured hosts drew level thanks to a bizarre mistake from Napoli keeper Reina.
The Spaniard somehow failed to keep hold of Ibrahima Mbaye's weak close-range effort, gifting 18th-placed Livorno a point that moves them level with Chievo.
Napoli were without suspended top scorer Gonzalo Higuain, but almost took the lead in fortuitous fashion after 10 minutes when Mbaye deflected the ball against his own bar following Marek Hamsik's surge into the box.
Winger Mertens then forced home goalkeeper Francesco Bardi into the first save of the match with a tame effort from the edge of area as Napoli began to take control of proceedings.
Benitez's men continued to dictate matters without creating many clear-cut opportunities, although Mertens did test Bardi's reflexes again when the Belgian cut in from the left only to see his strike punched away.
And Mertens’ perseverance was finally rewarded just after the half-hour mark, as the visitors were awarded a penalty for Federico Ceccherini's ill-advised shove on Goran Pandev.
Former PSV Eindhoven man Mertens made no mistake from the spot, coolly slotting the ball into the bottom corner for his sixth league goal of the season.
Livorno would have fallen further behind shortly after if not for the reflexes of Bardi, who denied Jose Callejon with a fine low save.
However, Di Carlo's side equalised against the run of play on 39 minutes, Mbaye atoning for his earlier lapse when he flicked Djamel Mesbah's cross towards Liverpool loanee Reina, who allowed the ball to slip from his grasp and over the line.
Both sides created openings early in the second half, with Livorno's top scorer Paulinho volleying straight at Reina from point-blank range before Bardi produced a good save to keep out Hamsik's header.
Mertens remained the most dangerous player on the pitch, though, and he came close to restoring Napoli's lead just after the hour mark, only for his left-wing cross-cum-shot to drift narrowly wide of the post.
Benitez's team created the better opportunities in the closing stages, with Callejon shooting wide from the edge of the area late on, but they could not find a way through the stubborn home defence as Livorno held on for a creditable draw.
