Visay Phaphouvanin scored two goals, including one on a penalty kick in the 79th minute, and the Laos booters preserved the stunning win at the Bacolod City Sports Complex.
"This is good news for our country. This is big considering the fact that were ranked lower than Myanmar," said Laos coach Valeriv Valirey, a Russian, through an interpreter.
Myanmar, a semifinalist in the Vietnam Games two years ago, actually converted an inside-the-box tight shot through Soe Myat Min towards the end but it was ruled off-side by the linesmen.
In an earlier play, Khin Maung Tuns potential game-tying short header bounced off the bar to the big disappointment of the Myanmar bench and its sizeable crowd in the venue formerly known as Paglaum.
Laos set out as the underdog being last-placer in its group in the Vietnam Games and a no-show in the pre-SEA Games tournament in Bangkok last October.
However, the Laotians gave their Myanmar rivals a big surprise, coming out aggressive and dominating the early goings with Bavone Vongsamany breaking the ice by eluding Myanmars last defensive line for a simple roller in the eighth minute.
Myanmar drew even at 1-all on a cross shot by Min off an assist by Yan Paing in the 19th minute.
After the break, Laos seized the initiative again with Phaphouvanin scoring his first goal in the match in the 65th minute.
Myanmar equalized for the second and last time also on a tap-in by Chanthalome Putthadavong with nine minutes left in the clock as action turned rugged on the turf.
Vietnam rallied from 0-1 deficit to beat Singapore, 2-1, in a Group of Death match in the second game. Phan Van Nguyen delivered the goals for the Vietnamese.