Muguruza, competing in her first tune-up event for the August 27-September 9 US Open, appeared to be heading for a routine victory after rolling through the first set and jumping ahead 3-0 in the decider but Tsurenko had other plans.
Tsurenko stormed back to go ahead 5-4 and sealed the contest on her first match point when a Muguruza forehand from behind the baseline sailed long, giving the Ukrainian world number 44 her first top-10 victory since 2015.
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The victory provided some measure of revenge for Tsurenko, who retired hurt just two games into her round of 16 match with Muguruza at this year's French Open.
Next up for Tsurenko is a clash with Ekaterina Makarova as the Russian topped Frenchwoman Alize Cornet 6-2 6-0.
Joining Tsurenko in the third round is US Open champion Sloane Stephens, who enjoyed a routine 6-3 6-2 win over German Tatjana Maria.
Stephens, who finished runner-up to world number one Simona Halep in Montreal on Sunday, continued her fine form on the North American hard courts and controlled the tempo throughout her 71-minute match.
Stephens will next face Elise Mertens after the 15th-seeded Belgian earned a 3-6 6-2 7-6(1) win over Swedish qualifier Rebecca Peterson.
Also advancing to the third round was Belarusian Aryna Sabalenka, who upset Czech ninth seed Karolina Pliskova 2-6 6-3 7-5, and Australian Ashleigh Barty, a 7-5 6-3 winner over Estonia's Kaia Kanepi.
Top seed Halep, looking to go one better than her runner-up showing in Cincinnati last year, will lead off the evening session with a second-round match against Australian qualifier Ajla Tomljanovic.
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Muguruza overpowers Badosa to reach final