Yuki saved all six break points he faced en route to a close 6-4 6-4 win in the quarterfinal contest which lasted one hour and 29 minutes.
The 23-year-old Indian managed to break his experienced rival from Uzbekistan once each in the two sets and that proved to be crucial in the outcome of the match.
It was the second time that Yuki played Dustov, having lost to the 29-year-old in the 2012 Davis Cup tie on clay.
Later in the day, Yuki and his Kiwi partner Michael Venus reached the doubles final when their opponents Marius Copil and Jurgen Melzer handed them a walkover due to latter's shoulder injury.
In singles, Yuki next faces Israel's seasoned Pro Dudi Sela.
"He too is a tough opponent but it is semifinals, so can't expect anything less," he said.
"I have always believed in my doubles ability but dont't play a lot.
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