Cheered on by the home crowd the world number eight eased through the first set but fell a break behind in the second before upping her game to avoid a deciding set.
"I only had one little dip but I tried to stay strong. I felt I was able to raise my game," Konta, who will carry Britain's hopes in the Wimbledon women's singles next month, said after reaching the semis without dropping a set.
"It was definitely a nice little comeback," Konta added. "I worked very hard to get myself back into that second set and stop Ashleigh from running away with it."
Konta won a round at Wimbledon for the first time last year after four opening round defeats but after her rapid rise up the rankings, including the title in Miami this year, she will be expecting a deep run at the All England Club.
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She will continue to sharpen her game with a Saturday semi-final in Nottingham against Magdalena Rybarikova who beat American qualifier Kristie Ahn.
Croatia's Donna Vekic, a former finalist at the Birmingham grasscourt event, also reached the last four with a 6-2 6-3 defeat of Greek player Maria Sakkari.
(Reporting by Martyn Herman; editing by Jeremy Gaunt)
