The Partenopei travelled to Turin at the back of a three-game winless run in all competitions, but the defender set the tone for the tie with an early opener.
In the fourth minute, the 26-year-old powered the ball past Salvatore Sirigu from Allan's flick, off a Jose Callejon corner kick. While Piotr Zielinski and Marek Hamsik added two goals in the 25th and 30th minutes respectively.
Andrea Belotti's strike in the 63rd minute was mere consolation for Sinisa Mihajlovic's side as their visitors ran out 3-1 victors.
The goal was Koulibaly's third of the season in 16 Serie A appearances. His side are now at the summit of the Italian top-flight log with 42 points from 17 encounters.
Maurizio Sarri's side welcome Udinese to the Stadio San Paolo for their next league outing on Tuesday.