The result sent Emerse Fae's side into the World Cup knockout stages for the first time in history and ensured the debutants finished bottom of the pile.
Les Elephants only needed a point to finish as runners-up, but they took control early on and went in front inside seven minutes when Liverpool target Yan Diomande took advantage of Curacao failing to clear their lines to square for Pepe, who slotted smartly into the bottom right corner.
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It should have been 2-0 before the 20-minute mark but under pressure, Amad Diallo scuffed another Diomande cross wide.
Curacao did not lose spirit, with Jurien Gaari, Tahith Chong and Leandro Bacuna all managing shots, but a combined xG of just 0.13 illustrated the lack of definitive threat they carried.
While they trailed by just one goal, Dick Advocaat's side possessed the more urgency of the two teams after the break - until their hopes suffered a hammer blow just after the hour, when Ibrahim Sangare set Pepe free in the box with a glorious ball.
He opened his body and coolly fired a second past Eloy Room that secured Ivory Coast's historic progression and broke Curacao hearts.
