Ismail Al Ajmi's first-minute strike proved decisive as goalkeeper Ali Al Habsi and the crossbar denied the hosts.
"We still have a chance. We never give up," insisted Thailand coach Charnwit Polcheewin.
Amad Al Hosni stunned the hosts when he raced into the Thai half and crossed to Ismail Al Ajmi, who coolly slotted home as fans were still taking their seats.
"We wanted to wait for Thailand to come, and then we counter-attacked," said Oman's Uruguayan coach Julio Cesar Ribas. "To win three points away from home is hugely important. We can now continue fighting for qualification."
Dangda Teerasil nodded a corner onto the crossbar and Oman goalie Al Habsi acrobatically clawed away a goal-bound follow-up header as the hosts pressed.
The towering Al Habsi, who had been expected to miss the trip to stay with relegation-threatened Bolton Wanderers, was key to the win as he made several vital saves including from Punnarat Kinsukon's long-range shot.
And the visitors nearly hit Thailand on the break on 67 minutes as Mohamed Almabi made a surging run from his own half, beat two Thai defenders, and unleashed a powerful drive that rebounded off the crossbar.
Thailand were badly in need of a win following their 4-1 hammering by Japan in their first game. But the victory breathes new life into Oman's qualifying campaign after their 1-0 defeat to Bahrain last month.
Thailand have historically performed well at home, losing just twice in Bangkok in the past two years prior to Wednesday.