Juventus, chasing a seventh successive title, still face hard matches away to Inter Milan and AS Roma. "I have seen a lot in football. anything can happen".
Ciro Immobile scored a brace as Lazio crushed Sampdoria 4-0 to stay fourth, just behind Roma who warmed up for next week's Champions League semi-final against Liverpool with a 3-0 win at SPAL on Saturday.
The Azzurri nearly saw things through for the point that would have kept them out in front heading into the final stretch, but Koulibaly met Jose Callejon's corner to win the match for Napoli at the death.
However, before Napoli had even entered the Juventus Stadium, their manager did something to show exactly how he feels about the reigning Italian champions.More news: Shania Twain says she would've voted for Trump, later apologizes
Napoli have only ever won two Serie A titles, both with Diego Maradona in their side, most recently in 1989-90.
"We gave our fans a huge joy today that goes above and beyond the standings".
Juventus lost Giorgio Chiellini to injury and his absence could be crucial over the next four games.
The Light Blues continued control possession in the game as the second half went on, but Allegri's men were impenetrable at the back, even in the absence of Chiellini.
Napoli did have the ball in the back of the net after 37 minutes, but the strike was ruled out after Lorenzo Insigne was flagged offside.More news: Brandon Belt breaks Major League Baseball record for longest at-bat, goes 21 pitches
The Italy forward tapped in a ball from Sergej Milinkovic-Savic five minutes from time and doubled his tally moments later after running onto Luis Nani's through ball.
Immobile leads Serie A scoring with 29 goals, three more than Inter forward Mauro Icardi.
However, Miralem Pjanic hit the post in the first half with a deflected free-kick.
Inter broke the deadlock seven minutes after the break.
But he was quick to remember that Juve remained one point clear with four matches to play.More news: Kathua victim was sexually assaulted, her hymen was not intact: Crime Branch
Elsewhere, Cagliari drew 0-0 at home to Bologna and Atalanta beat Torino 2-1 to move above Milan and into the Europa League spots.