Young, ranked 56th in the world, withstood 11 aces from the 24th-ranked Dolgopolov in a match lasting one hour and 56 minutes.
“I thought I fought well,” said the American, who remains in search of a first ATP tour title.
“I didn’t start off the way I wanted to. He was playing pretty well, hitting through the wind and controlling his shots quite good. I decided to buckle down, fight, go out swinging and got a little more not so conservative and it happened to work.”
Young reached his fifth tour-level semi-final and his second in as many weeks after making the final four at Memphis.
Tomic, playing his fourth quarter-final of the season, ended the run of 19-year-old Japanese qualifier Yoshihito Nishioka 6-3 6-1.
Tomic saved all seven break points he faced to dismiss the 154th-ranked Nishioka in less than an hour.
Taiwan’s Lu Yen-Hsun, who toppled top-seeded South African Kevin Anderson, takes on fifth-seeded Adrian Mannarino of France while fourth-seeded Croatian Ivo Karlovic faces seventh-seeded American Steve Johnson for a place in the last four.