The 2016 French Open champion took two hours and five minutes to defeat Kuznetsova, herself the 2009 champion, for the sixth time out of seven career encounters, reports Efe.
Muguruza struggled early in the match, with the score at 5-5 when the game was paused after a little over an hour due to the weather.
When play resumed, Muguruza rallied and went on to sweep the Russian world No. 43 in the following tiebreak 7-0.
Despite Kuznetsova's strong showing in the second set, Muguruza turned up the heat and sealed her place in the next round, where the former world No. 2 is to square off against Fiona Ferro of France, who beat Germany's Carina Witthoft 6-4, 6-2.
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