Stefano Lilipaly struck in the 85th minute after fellow midfielder Andik Vermansah brought Indonesia back into the game with a goal on the hour.
They had gone behind in the Group A match after Singapore forward Khairul Amri scored in the first half.
Thailand, already through to the semi-finals, eliminated the disappointing hosts Philippines from the biennial tournament with a late Sarawut Masuk strike, the only goal in the other Group A match.
Indonesia play the winners of Group B in a home-and-away format on December 3 and December 7.
The Group B runners-up will play Group A leaders Thailand in the other semi-final on December 4 and December 8.
On Saturday, all eyes will be on the Myanmar-Malaysia match in Yangon to decide who joins Group B leaders Vietnam in the semi-finals.
Both Myanmar and Malaysia are on three points but with Myanmar having a superior goal difference.
In the other group match on the night Vietnam, on six points, play Cambodia who were already eliminated.