Les Éléphants crashed the party on Thursday to make it out of their group for the first time in four World Cup appearances.
Ivory Coast beat Ecuador 1-0 in their tournament opener - at the same Philadelphia stadium as Thursday's game - and lost to Germany in their Group E second game.
Ivory Coast will now meet either France or Norway, whoever is the runner-up in Group I on June 30.
Curaçao needed to win and instead failed to become the smallest nation to qualify for the knockout stages.
Pépé, who plays for Spanish club Villarreal, wiped out all the suspense early, scoring in just the seventh minute and they led the rest of the game in front of an enthusiastic crowd that made Les Éléphants feel at home.
Ivory Coast held their training base in nearby Delaware and practised at the Philadelphia suburban home of Major League Soccer's Philadelphia Union.
Throw in a friendly against the Union's second team, and the thrilling win in the 90th minute against Ecuador, and Les Éléphants found their adoptive fans among the crowd of 68,324 - about 40 per cent of the population of Curaçao.
The fans in Ivory Coast orange went wild when Pépé scored again with a left-footed shot from the far corner in the 64th minute to seal the win. He was subbed out three minutes later to earn some rest for the June 30 game that will serve as their biggest ever.
Ivory Coast needed only a draw to advance yet played with a competitive fire the rest of the game and never let Curacao get close to scoring.
Ivory Coast pounced when 19-year-old Yan Diomande, who came to America four years earlier as a soccer prospect who couldn't speak any English, snared the ball when Curacao failed to clear it and fed it to Pepe for the easy goal past Eloy Room.
The 37-year-old Room had made 15 saves against a relentless Ecuador attack and helped The Blue Wave earn their first-ever point with a 0-0 draw on Saturday.
But the historic clincher belonged to Pepe and he was named player of the game.
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