Praweenwat Boonyong's 23rd minute penalty kick sent Thailand to their first final since 2007.
In tomorrow's final, Kiatisak Senamuang's men will meet Indonesia who stunned Malaysia 4-3 on penalties after a 1-1 draw in yesterday's other semi-final.
Thailand hammered the Indonesians 4-1 in the first round of the Myanmar Games.
Thailand were eliminated in the last two tournaments in 2009 and 2011 and Kiatisak is confident that his men will end the title drought.
''Our aim is to win the gold medal,'' said Kiatisak.
''But we have to work hard to win the title. Our win against Indonesia in the first round is irrelevant.''
At Zeyar Thiri Stadium in the country's new capital, Singapore were the better side in the opening minutes but once Thailand found their rhythm they dominated for long periods.
The Thais broke the deadlock after 23 minutes when Thai-Swiss midfielder Charyl Chappuis won a penalty after he was tripped in the area.
Bangkok Glass FC defender Praweenwat made no mistake from the spot.
The Young Lions then piled the pressure on Thailand but failed to break their defence marshalled by captain Theerathon Bunmathan.
Thailand started the second half strongly forcing Singapore goalkeeper Muhammad Mahbud to make a couple of saves.
But the game then became uneventful and the Thais chose to defend their lead.
The match became lively again in the final 10 minutes as Singapore threw everything at Thailand but could not beat goalkeeper Kawin Thamsatchanan.
In yesterday's first semi-final, Indonesia beat Malaysia 4-3 on penalties following a 1-1 stalemate, avenging their defeat to their arch-rivals in the 2011 final in Jakarta.
The game finished 1-1 in normal time with a late goal from forward Thamil Arasu cancelling out a spectacular strike from Bayu Gatra after 30 minutes of a game which the Indonesians dominated.
Extra-time was a dour affair with both teams flagging on the large pitch.
The win was sweet revenge for the Indonesians, who lost on penalties to their neighbours in the final of the 2011 Games.
The Malaysians were bidding for their third straight SEA Games gold in the showpiece event of the hotly contested competition.
Indonesia, who broke the hearts of local fans with a narrow 1-0 win over Myanmar to progress from the group stage at their expense, will play Thailand in the final of the under-23 tournament.
Against Thailand tomorrow, Indonesia will try to end their SEA Games hoodoo after going more than two decades without winning gold in the biennial tournament.