March 26, 2017 1109 GMT
World number 10 Konta triumphed 6-3 7-5 against Russian 19-year-old Daria Kasatkina, who beat world number one Angelique Kerber in the previous round, BBC reported.
The 25-year-old will face Canadian Eugenie Bouchard in the last four.
Evans, 26, beat Spanish eighth seed Marcel Granollers 1-6 6-3 6-3 to reach the third round.
He will face the winner of the match between top seed Dominic Thiem of Austria and Portuguese qualifier Gastao Elias.