Nchout turned inside Ria Percival in the 95th minute and superbly curled in the winner to put Cameroon through.
They were heading out after Aurelle Awona sliced a volley into her own net with 10 minutes remaining for 1-1.
Nchout had put her side ahead in the second half with a lovely, dinked goal.
Although Cameroon finished on three points, the same as Nigeria from Group A, they went through courtesy of a better fair-play record between the two African sides.
The Netherlands finished top of Group E with a 100% record after a 2-1 victory over Canada, who finish in second place.