Konta, on Wednesday, needed one hour and 22 minutes to get her second career victory against Suarez Navarro, who is ranked 29th in the world, reports Efe.
In other action, Romania's Sorana Cirstea stunned Belgium's Elise Mertens 6-5, 6-4 and will face Spain's Garbiñe Muguruza, the No. 4 seed, next.
Muguruza knocked off China's Duan Yingying, 6-3, 6-4.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)