Kerber, the top seed and two-time runner-up, overcame qualifier Kristina Kucova 7-6 (7-4) 6-2 on the hard-courts in Mexico.
The German's two final defeats at the WTA International event have come to four-time champion Anastasia Pavlyuchenkova.
Pavlyuchenkova started her bid for a fifth crown with a 6-0 6-3 thrashing of Russian compatriot Anna Blinkova.
Meanwhile, defending champion Muguruza was tested before getting past Romanian Elena-Gabriela Ruse 6-4 7-6 (7-4).
Also in Monterrey, two-time grand slam champion Victoria Azarenka eased through her opener against qualifier Miyu Kato 6-4 6-2.
Kristina Mladenovic battled through, while the only seed to fall was Alison Riske, who was beaten by Sachia Vickery 7-6 (8-6) 6-1.
At the Charleston Open, former champions Sloane Stephens and Kiki Bertens reached the third round.
Stephens, the 2016 winner struggling for form so far this year, battled past Sara Sorribes Tormo 7-6 (7-4) 7-6 (7-4).
Bertens, the defending champion and second seed, had fewer problems, crushing qualifier Martina Trevisan 6-2 6-1.
In first-round matches, the likes of Kaia Kanepi, Danielle Collins and Andrea Petkovic won through.