Norrie, 23, enjoyed a straight-sets victory over South Korea's Kwon Soon-woo, with the British number two beating the world number 117 6-3 6-4.

Evans, ranked one place below Norrie at 55, then triumphed in a hard-fought match with world number 42 Radu Albot.

The 29-year-old, who reached the third round at Wimbledon this month, beat the Moldovan 7-6 (7-5) 5-7 6-2.

Norrie will now face Alexei Popyrin for a place in the last four after the 19-year-old Australian upset world number 39 Pierre-Hugues Herbert, beating the Frenchman 7-5 6-3.

Evans will play Reilly Opelka who beat fellow American John Isner, last year's Atlanta Open champion, 7-6 (7-2) 6-7 (5-7) 7-6 (7-5).