The in-demand Cote d'Ivoire winger scored his 18th league goal of the season while the 27-year-old registered his third goal this term in the encounter.
Valentin Eysseric opened the scoring in the in the 54th minute from the penalty spot and two minutes later Coulibaly doubled the lead for the Canaries.
In the 62nd minute, Rafael Leao halved the deficit and four minute after Pepe levelled proceedings for his side, converting from the penalty spot.
Jonathan Bamba then scored the winning goal for Christophe Galtier’s men in the in the 69th minute to help them clinch their ninth away victory this term.
Coulibaly featured for the full duration of the tie while Pepe made way for Thiago Maia in the 90th minute.