Next up for Anisimova, ranked 130th in the world, is Wimbledon champion Muguruza, who will be eager to get back to competition after falling at the first hurdle in Indian Wells.
Brazilian Beatriz Haddad Maia overcame some early pressure to defeat Briton Heather Watson 7-6(3) 6-2. Watson had a chance to serve for the opening set but squandered it and then allowed the Brazilian to run away with the match.
Haddad Maia will next face No. 31 seed Zhang Shuai.
Australia's Ajla Tomljanovic looked headed for an early exit when she fell behind 4-0 in the deciding set against Ukraine's Lesia Tsurenko but the Croatian-born world number 90 reeled off seven of the next eight games to prevail 3-6 6-4 7-5.
American wild card Bernarda Pera advanced when she stunned Spanish world number 68 Lara Arruabarrena 7-5 6-4 to set up a second-round match with Belgian 22rd seed Elise Mertens.
Estonia's Kaia Kanepi was leading Christina McHale 3-1 but retired 31 minutes into the match, gifting the American passage into the second round where she will face Czech Barbora Strycova.
Also advancing on the first day of the main draw in Miami were Belgians Kirsten Flipkens and Alison Van Uytvanck, Swede Johanna Larsson, Hungary's Timea Babos, Belarusian Aliaksandra Sasnovich and American wild card Claire Liu.
(Reporting by Frank Pingue in Toronto; Editing by Peter Rutherford)
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