The Partenopei looked set to be forced to settle for a draw that would leave them four points behind the reigning champions after a tense contest in Turin on Sunday.
Centre-back Koulibaly had other ideas, though, rising to power home Jose Callejon's corner in the last minute of regulation time and see Maurizio Sarri's side move to within one point of the leaders with four rounds of the season remaining.
Speaking to Mediaset Premium, the hero of Napoli's first victory at Allianz Stadium was adamant they have always backed themselves to keep the pressure on Massimiliano Allegri's men.
"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," Koulibaly said.
"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.
"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.
"There is one point [between us]… we want to win every game from now to the end.
"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."