Bhambri got the better of Korea's Duckhee Lee, the third seed, 7-5, 6-2 in one hour and 25 minutes while Thompson beat unseeded Spaniard Pedro Martinez 6-1, 7-6.
The first set saw an even contest between the Indian number one, ranked 112 in the world and the speedy Korean. Bhambri played well within himself from the baseline and made the occasional foray to the net to finish off points.
A solitary break did the trick for Bhambri, a former Australian Open junior champion, in the first set.
The Indian ace didn't face a single break point through the course of the match.
With the win, Bhambri improved his head-to-head against Lee to 2-0 and enhanced his chances of returning to the top 100.
In the other semifinal, Thompson started the match with two aces in the first game and dominated the set, taking it 6-1 in quick time.
The Spanish player, who upset fourth-seeded Egyptian Mohammed Safwat in the quarterfinals, fought back in the second and held his own against the Aussie.
The No.1 seed kept his composure to take the tie-breaker to progress to tomorrow's final.
Results: Singles (Semifinals): Jordan Thompson (Australia-X1) beat Pedro Martinez (Spain) 6-1, 7-6; Yuki Bhambri (India-X2) beat Duckhee Lee (Korea) 7-5, 6-2.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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