Thailand won the second leg 1-0 but Singapore, who led 3-1 from Wednesday's home leg, defended resolutely in a sweltering Bangkok to protect their advantage.
Singapore rarely troubled the hosts, who paid the price for errors in the first leg and squandering chances in the second.
"In the end, we fully deserved this. The final was over two legs and we dominated the first," Singapore coach Radojko Avramovic said.
"We predicted they would play this way but we lost the ball every time in their half while Thailand were always trying to break us down.
"We had some luck. I don't think Thailand were losers here."
The game was lively but often clumsy, with Thailand undermining their cause with poor finishing.
In an action-packed first half, Jakkapan Pornsai's header hit the post, Teersil Dangda tripped in front of goal, and Kirati Kaewsombut headed wide from close range.
The pressure told on the stroke of halftime, when Kirati scored with a powerful header from a corner.
Thailand still needed a second goal, and Pipob On-Mo and Chanathip Songkrasin came close, while Kirati turned two defenders before scooping his effort agonisingly over the bar with only the keeper to beat.
"I don't like second-best," said Thailand's German coach, Winfried Schaefer. "But I'm proud of this team: we showed good spirit, good character, good teamwork."