It was first win over a top-100 player this season for the 273-ranked Indian, who outplayed the Ukrainian 6-2 6-4 in one hour and 10 minutes.
Stakhovsky rose to fame in 2013 when he downed legendary Roger Federer in a gruelling second round match at the Wimbledon. He has won four ATP World Tour singles titles but has not won any trophy since New Haven in 2010.
"Everything came together today. I wanted to focus on my service games and take a few chances on his serve because he serves well. Thankfully those paid off. I am happy for the fact that I did not take my foot off the gas as it is important to keep pressing specially against good players," Yuki told PTI after his match.
It will be third semifinal of season for Yuki on the ATP Challenger Tour, having reached the last-four stage of Zhuhai and Shenzen events in March.