Pépé opened the scoring in the seventh minute when Yan Diomandé capitalised on slack Curaçao defending to play the Villarreal forward in for a close-range finish. The game was settled in the 64th minute when Ibrahim Sangaré's precise pass found Pépé in the box and he curled a composed finish into the top-left corner.
Ivory Coast needed only a draw to advance and will now face France or Norway in the round of 32. Curaçao finish bottom of Group E without a win.
Pépé said the result gave him both personal satisfaction and collective pride.
"It's a source of pride and joy. We've qualified for the knockout stage, so for the people of Côte d'Ivoire, this is a source of pride," he said.
"My two goals? It's all thanks to the team. On the first one, Yan did a great job setting me up with the ball.
"The second was a magnificent pass from Ibra, and all I had to do was get my foot on it."
He made clear the celebrations will be measured.
"It's one game at a time. We're going to try to go as far as possible — we have the players and the quality to do it. We'll need to stay focused, rest up, and see who we'll be playing against."
Head coach Emerse Fae framed the moment in terms of what it means for the country.
"Pride is the first word that comes to mind. We knew we could do it, and we also knew it was going to be difficult. We did it. On top of that, we finished second."
He addressed supporters directly.
"Ivory Coast deserves this, can enjoy it, and can celebrate tonight. They can keep cheering us on so we can go as far as possible."
At 31, Pépé became the second-oldest African player to score a brace at a World Cup, after Roger Milla, who scored two braces at the age of 38 for Cameroon at Italia 90. It is also only the second time Ivory Coast have won two matches in the same World Cup tournament.
The 2026 tournament is Ivory Coast's fourth World Cup appearance. Their previous campaigns in 2006, 2010 and 2014 all ended without reaching the knockout rounds.