The War Elephants led 1-0 when the Buriram United forward netted the first goal 26 minutes into the match.
Supachai then scored another goal three minutes into the second half at Abdullah bin Khalifa Stadium in Doha.
It was Thailand coach Masatada Ishii’s first win in competitive matches, reports the Bangkok Post.
Thailand’s next game will be against Oman on Sunday.
Ishii on Monday urged the War Elephants to put in their best effort when they took on Kyrgyzstan.
Thailand are the lowest ranked team in Group F that includes former champions Saudi Arabia and Oman.
In the other game in Group F yesterday, Saudi Arabia beat Oman 2-1.