The Mali striker scored his seventh league goal this season to help the Canaries extend their winning run to five games.
Abdoulaye Toure opened the scoring in the 51st minute with an assist from Valentin Rongier.
In the 73rd minute, Dijon suffered a setback after Nayef Aguerd received his second yellow card and was subsequently sent off.
Coulibaly then converted from the penalty spot to double the lead for the Canaries before Rongier sealed the win with 10 minutes left to play.
The Mali international was on parade for the duration of the game as Vahid Halilhodzic’s men secured their 13th win of the season.
With the result, Nantes climbed to 11th spot on the table with 46 points from 35 games.
The Eagles are in Group E alongside Angola, Mauritania and Tunisia.