The sixth-seeded Cornet, who won the event in 2016 and hasn't dropped a set this year, overcame a fall and skinned knee to reach the semifinals. Cornet served for the match at 5-2 in the second set but was broken as Minnen hit some clean winners.
"To finally close it out at 5-4, I was pretty tight, so I'm happy I could finish the match," Cornet said. "To be in the semifinal is a great start to the year." Cornet will next play Sofia Kenin for a place in the final. The 20-year-old American beat veteran Kirsten Flipkins 7-5, 7-5.
In other quarterfinal matches, Belinda Bencic beat Dayana Yastremska 7-6 (2) 6-3 and Anna Karolina Schmiedlova defeated Irina-Camelia Begu 7-5, 7-5.
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