Curacao had a nervous wait after the early match in Group C, but their progression was confirmed when El Salvador crashed out with a 4-0 loss to Honduras in the late contest.
The latter result put Jamaica top of the group on five points, with Curacao, population 160,000, claiming second on goal difference ahead of third-placed El Salvador.
Jamaica will play the runner-up of group D, either the United States or Panama, who are locked on six points ahead of their match on Wednesday, the U.S. with a vastly superior goal difference.
Curacao will meet the winner of Group D.
Shamar Nicholson scored for Jamaica in the 14th minute with quick reflexes but could have had a hat-trick by then, having already missed a point-blank header and sent a shot crashing against the post.
Jamaica squandered several other chances, while Jarchinio Antonia missed a great opportunity for Curacao late in the first half when he dragged a shot wide.
Just when it seemed Jamaica would not pay for their profligacy, Curacao equalised in the 93rd minute when defender Gaari smashed a 25-yard strike into the corner after being set up by Leandro Bacuna.
Curacao almost completed a smash-and-grab victory when substitute Elson Hooi missed a long-range shot by millimetres with virtually the last kick of the match.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Ian Ransom)