The seventh seed overcame tough resistance from former top-10 player Kateryna Bondarenko in the first set, saving two set points at 4-5 before prevailing 7-2 in the tiebreak.
With the first set in her back pocket, the Brit displayed more confidence in the second set, never facing a break point. She would go on to defeat the Ukrainian 7-6(2) 6-2 after an hour and 45 minutes.
Watson next faces Christina McHale, who rallied past Caroline Dolehide 5-7 6-4 6-3 in an all-American second round battle.
Canadian teenager Leylah Annie Fernandez upset eighth-seeded Nao Hibino 6-3 6-0 to reach her first WTA main draw quarterfinal. After being selected to represent her nation at the Fed Cup Qualifiers earlier this month, the defending French Open girls singles champion has been having an exceptional season.
Fernandez will meet fellow teenager Anastasia Potapova in the quarterfinals, as the Russian youngster defeated German veteran Tatjana Maria 6-3 6-3. This will be the first meeting between both ladies at the WTA Tour-level.
Former world No.5 Sara Errani's comeback was halted by China's Xiyu Wang. The Hua Hin quarterfinalist outlasted Errani 7-5 6-7(3) 6-1 to advance to her second Tour-level quarterfinal of the season.
Sixth seed Lin Zhu of China defeated Brit Katie Boulter 7-6(2) 7-5 in an hour and 48 minutes, while Slovenian Tamara Zidansek breezed past compatriot Kaja Juvan 6-2 6-2.
Home favorite Renata Zarazua continued her dream run, fighting from a set down to defeat American qualifier Katie Volynets 4-6 7-5 6-0. After upsetting top seed Sloane Stephens in the first round, Zarazua's confidence and popularity have risen as she continues to do the host nation proud.
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