Host Thailand won the first two sets 25-17 and 25-23 and their World No. 8 opponents took the third set 20-25 before Thailand sealed victory with a 25-22 win in the fourth set at the packed Hua Mark Indoor Stadium in Bangkok.
World No. 12 Thailand now has five points from seven matches in the FIVB World Grand Prix, a 28-country tournament in which six teams will advance to the finals in Tokyo on Aug 24.
The win was only the second for the Thai team after an upset of seventh-ranked Serbia in South Korea two weeks ago.
Thailand's task will only get harder on the weekend as it faces the world's two best teams, starting with the United States (No. 2) on Saturday and No. 1 Brazil on Sunday.
"Today was not an easy game," said Thailand coach Kiattipong Radchatagriengkai. "I admire the Dominican team spirit. They are very capable players but I think they still might be tired from the long trip. I wish the Dominican team success in their upcoming matches."
"This was not an easy game to win, we had many errors and lost many points continuously," agreed Thailand captain Wilavan Apinyapong. "There are many things we need to improve from this match. The Thai volleyball fans encouraged us in the hall which was a big advantage. We have to study today’s match and prepare for the game with USA tomorrow."