The world number 594 will have more than 14 hours to think about the possibility of a huge upset before serving for the match when play resumes on Friday.
Sixth seed Muguruza, meanwhile, drew a blank in the first set of her match against 46th-ranked American Christina McHale, who led 6-0 2-3.
Earlier, Czech second seed Karolina Pliskova cruised into the third round with a 6-1 6-3 win over Madison Brengle, while Dominika Cibulkova beat Paraguayan qualifier Veronica Cepede Royg 6-3 6-2.
Pliskova, a finalist at last year's U.S. Open who reached the semi-finals at Indian Wells last week, relied on her booming groundstrokes and strong returning to dispatch her American opponent in 59 minutes.
"The last few matches it's not really about my serve because the percentage is a little low, but I'm happy that I have my game from the baseline," Pliskova, who hit 27 winners compared to six for Brengle, said after the match.
"I was feeling the ball pretty well today."
Pliskova controlled the rallies, winning six straight games to finish off the opening set and go up a break in the second.
Brengle then attacked Pliskova's serve to earn her first service break, but the world number three re-established the lead in the next game and served out to end the match.
Slovakian fourth seed Cibulkova faced only two break points against Royg and saved both in a win that set up a third-round clash with Belgian Kirsten Flipkens, who outbattled 29th seed Croatian Ana Konjuh 7-6(4) 6-7(6) 6-2.
Fifth seed Agnieszka Radwanska of Poland survived a first set tiebreak before dusting off China's Wang Qiang 7-6(3) 6-1.
Twelfth seed Caroline Wozniacki of Denmark was impressive in a 6-1 6-1 demolition of American Varvara Lepchenko 6-1 6-2.
(Reporting by Andrew Both in Cary, North Carolina and Frank Pingue in Toronto; Editing by Larry Fine and Nick Mulvenney)
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