Following a goalless first-half, the Mali striker broke the deadlock in the 49th minute after he was set through by Ghana international Majeed Waris to put the Canaries on the path of victory.
Six minutes later, the 27-year-old doubled his side’s lead after benefitting from Lucas Lima’s assist.
Moments before the hour mark, Valentin Rongier scored the third goal for the hosts to help Vahid Halilhodzic’s men clinch their 11th win of the season despite strikes from Juan Otero and Cheick Timite.
Coulibaly featured for the entire duration of the game while South Africa’s Bongani Zungu ended on the losing side. The Bafana Bafana midfielder played for 59 minutes.
With the win, Nantes moved to 13th spot in the league standings after garnering 40 points from 33 games.
Coulibaly has six goals for Nantes in as many appearances and will hope to continue with his outstanding displays in their next game against Marseille on April 28.
The Eagles are in Group C along with Angola, Tunisia and Mauritania.