World number 10 Muguruza, who had only won two tour-level matches since the start of March, was tested in a gripping second-set tie-break by Magdalena Frech, eventually triumphing 6-1 7-6 (9-7).
After the victory, Muguruza said she was pleased to have overcome challenging weather conditions to reach the next stage, saying: "I feel like I fought hard against the wind, and I haven't played many matches on grass either.
"I could see today that if I didn't fight as hard as I can, I wasn't going to win."
A minor upset saw 17th seed Alison Riske slip to a 6-7 (3-7) 6-3 7-6 (7-4) loss to Magda Linette, while Yulia Putintseva surged to a 7-5 6-1 win over Sara Sorribes Tormo and seventh seed Barbora Krejcikova saw her contest with Marta Kostyuk halted by darkness at one set apiece.
Ajla Tomljanovic beat Aleksandra Krunic 6-0 4-6 6-3 and Heather Watson went down 7-6 (7-1) 6-4 to Canada's Rebecca Marino, as the Sussex crowds prepared for Serena Williams' eagerly anticipated doubles outing alongside Ons Jabeur on Tuesday.
There was frustration for Muguruza's fellow former Wimbledon champion Angelique Kerber at the Bad Homburg Open.
Kerber's match against Anastasia Gasanova got under way, but play was stopped due to fading light and a damp court after a rain-hit day. Third seed Kerber led 4-2 in the first set of a contest that will conclude on Tuesday.
The only other seed in action in Germany made routine progress, as France's Alize Cornet raced to a 6-2 6-4 win over Anna Kalinskaya.