It was the third defeat this season to six-time defending champions Juventus. It was also their second defeat at home, with the last loss dating back to November 19.
Juventus have 85 points from 34 games with Napoli, bidding for a third Scudetto after 1987 and 1990, on 84.
“We knew it was a very difficult and important match, but we did everything to win, we did it and can be proud of ourselves,” said 26-year-old Koulibaly.
“The city fired us up over the last few days and when we see all those fans accompanying us to the airport, it makes us very happy. We want to thank them and the best way of doing that was to win the game.”
Maurizio Sarri’s side pushed forward with numerous chances compared to Juventus who, apart from a Miralem Pjanic free kick hitting the post, had little to show.
Napoli captain Marek Hamsik threatend twice to break the deadlock while Lorenzo Insigne had a goal disallowed for offside in the first half with substitute Piotr Zielinski’s snapshot on 83 minutes cleared by goalkeeper Gianluigi Buffon.
“Juve are a very strong side, but we proved Napoli can fight it out with them. The team has always believed in the Scudetto and will do until it’s mathematically certain,” added Koulibaly.
“I had always lost playing here, but I am really happy, because we put so much into it. But the season isn’t over and if we need to give more, we’ll find more to give.
“We believe in ourselves, in our style of football, in our players and our staff. We proved that tonight.”
The champions now have a difficult run-in to the season against Inter Milan and Roma — both fighting for Champions League places.
Napoli will play Fiorentina, Sampdoria, Torino and Crotone in the final four matches.
In other results, Lazio and Inter Milan kept their push for Champions League football alive on Sunday.
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.
Roma and Lazio both have 67 points from 34 games with Roma ahead on head-to-head clashes.
Inter Milan are just outside the Champions League places in fifth one point behind after a hard fought 2-1 win over Chievo.
Lazio dominated Sampdoria in their Stadio Olimpico with Sergej Milinkovic-Savic breaking through after 32 minutes and a Stefan de Vrij diving header giving the hosts a second just before the break.
Immobile tapped in a Milinkovic-Savic assist five minutes from the end, quickly adding a second to consolidate his position as leading Serie A scorer with 29 goals this season.
Sampdoria, meanwhile, are now four points off the Europa League places with four games to play.(NAN)