It is the second ATP Tour semi-final of the 22-year-old Briton's career and the fifth seed will face Ryan Harrison for a place in Sunday's final.
The world number 45 was a break down in the first set when play was interrupted to give a fan medical help, but hit back to win nine of the last 10 games.
Harrison thrashed Christopher Eubanks 6-1 6-2 in their quarter-final.
American fourth seed Harrison said: "Kyle's been coming out. He was playing some amazing tennis at the end of last year and has shown some highlights of that throughout this year as well."

The doubles pair lost Monday's third-round match 6-3 4-6 6-4 3-6 14-12 to Jonny Marray and Adil Shamasdin.
The first code violation came after umpire Aurelie Tourte refused Cuevas a toilet break; the Uruguayan then showed his frustration at double-faulting.
"You have to take bad calls on the chin at some point," said Britain's Marray.
The earlier code violation was handed to Cuevas for unsportsmanlike behaviour when he threatened to wee into a ball can after being told he could not leave the court to visit the bathroom.
He then angrily smashed a ball out of the court following a double fault and the 15th seeds were docked a point, resulting in Cuevas and his partner sitting down and refusing to play the final game.
A supervisor had to be called.
"I went to the bathroom twice during the match and obviously the fifth set was a long one. I think you should be allowed an extra toilet break if it's five sets," said Marray.
"You have to respect the officials regardless of whatever happened in the match. You can have a word or two but they're trying to do a job and you have to respect that."
Shamasdin added: "I don't think the chair umpire really had the match controlled. She made a few mistakes early on at both ends. We were all on her and she was definitely flustered. I don't think she handled it correctly."
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Kyle Edmund defeated top seed Jack Sock 6-4 6-1 to reach the last four of the 2017 Atlanta Open.
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Pablo Cuevas and Marcel Granollers held a sit-down protest after receiving warnings for threatening to wee in a can and hitting a ball out of court.