Tomas Berdych and Jiri Novak beat Paradorn Srichaphan and Danai Udomchoke 6-3, 7-6, 6-4 to earn a 2-1 lead in the best-of-five match.
Everything now hinges on the battle between Novak and Paradorn in the first of Sunday's two matches.
Paradorn played a large part in Thailand's defeat as he struggled with his volleys and dropped serve four times.
Novak also failed to produce his best tennis, conceding his serve three times as his inexperienced partner held up the team.
Berdych, making his debut in the competition, dropped just three points on serve during his five service games in the opening two sets.
A crucial turning point came in the second set after Thailand had recovered from 5-2 down to force a tie-break.
Paradorn, who had double-faulted to lose the first set, netted the easiest of overheads at 2-4 to leave Novak serving out for the set.
"I was expecting a tough match and it's a surprise to me that we won pretty easily three sets to love," Novak said later.
"During the whole match we were doing much better on court. I'm very happy. We made the point and that's very important for our team.
"I think the pressure now is on Paradorn's side because they have to win both matches to win the tie. I'm playing great tennis and I have nothing to lose, because he is ahead of me on the computer and the pressure is going to be much more on him than on me."
