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)
