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|Jennifer Brady of USA returns the ball to Garbine Muguruza of Spain during the WTA Dubai Duty Free Tennis Championship. (KARIM SAHIB/AFP)|
The American who ranks just outside the Top 50 followed up on her first-round defeat of third seed and two-time champion Elina Svitolina at the Aviation Club.
"I was able to find a way, I wasn't feeling my best," Brady said after seeing off the ninth-seeded Spaniard.
"Maybe I didn't play my best tennis, but I stayed in there, competed and came out on top."
Brady will await a Friday opponent from top seed Simona Halep and number seven Aryna Sabalenka of Belarus, who defeated the Romanian last month in Adelaide.
Halep was tested but survived here on Wednesday against Tunisia's Ons Jabeur in three sets.
Brady made a recovery from a set down against two-time Grand Slam winner Muguruza.
The American secured the second set by breaking her opponent's last two serves.
She finished off the upset a set later on a second match point as Muguruza put a backhand over the baseline after almost two-and-a-quarter hours.
"I knew it was going to be hard because I've seen her play and she's having a good run," Muguruza who converted on only one of 10 break points, said.
"I had so many opportunities, I can't count how many I had. They didn't go my way.
"Every time I had an opportunity, she was playing well the point, serving big, making winners."
WTA match-win leader Elena Rybakina extended her total this season to 18 victories with a 7-6 (7/1) 6-3 win over number two seed Karolina Pliskova.
The Kazakh winner has been on a tear in 2020, winning the Hobart trophy and playing finals in Shenzhen and last weekend in in St Petersburg.
"It was tough match, the first time actually I played here in the heat. It was difficult," Rybakina said. "But I'm really happy that I made it."
Pliskova, a 2015 finalist, was still relatively pleased with her week.
"On days like this, really I didn't do that much wrong. Definitely I could have done some things better.
"I tried to be aggressive which with her is tough because you don't get that many chances.
"She was serving quite big. Conditions are fast, it was about a couple of points."