Benesova, of the Czech Republic, came from behind to defeat Russian Ekaterina Makarova 2-6, 6-2, 6-4.
Suarez Navarro, of Spain, breezed past Martina Muller of Germany 6-2, 6-0.
In other matches, Shuai Peng of China was a 6-4, 7-5 victor over Russian Vera Dushevina and Czech Lucie Safarova ousted American Jamea Jackson 3-6, 6-3, 6-0.
The semifinals will feature Benesova vs. Safarova and Suarez Navarro vs. Peng.
The hard-court tournament at the West Side Tennis Club in Forest Hills, N.Y., is a tuneup for the U.S. Open, which begins Monday.
Celebrity Couples of 2014 [PHOTOS]