It was a second meeting on the WTA tour for Britain's top two female players and, like the previous one in Indian Wells last year, Konta came out on top.
The windy conditions made life difficult for both but ultimately it was the extra power of Konta, who reached the final here 12 months ago, that made the difference in a 6-4, 7-6 (5) victory.
The fourth-seed Konta, who will face Dalila Jakupovic of Slovenia next, was the second British player to advance after a career-best win by wild card Katie Boulter over former U.S. Open champion Samantha Stosur.
Boulter won 7-6 (6), 6-1 to reach her first WTA quarterfinals, and is set to break into the world's top 50.
''She's a Grand Slam winner, and it's the first one of those that I've beaten,'' she said. ''I thought I held my nerve really well.''