"I think I learnt a lot from that match (at Indian Wells)," Muguruza said in an on-court interview. "I knew that it was going to be difficult, so I really trained hard and prepared."
Muguruza used a big serve to set up her booming forehand and took full advantage of Day's vulnerable second serve. The top-seeded Spaniard will next face fifth seed Ana Konjuh of Croatia, who battled past Russia's Natalia Vikhlyantseva 7-5 6-4.
The 23-year-old said she was doing her best to put the elation of Wimbledon behind her and focus on the hardcourt season.
"I'm just working on trying to forget what happened and just starting Stanford. Stanford is my goal and that's it," she told reporters.
American third seed Madison Keys survived a surprisingly stern test from teenage compatriot Caroline Dolehide to reach the last eight, rallying from a set down for a 3-6 6-2 6-3 win.
"I think I finally just took a big deep breath, and restarted the match and settled in a lot more," Keys said after overhauling the 212th-ranked 18-year-old qualifier.
"I wasn't playing great and I turned it around. Things are starting to look up and I'm really happy about that."
The victory set up a quarter-final meeting with seventh seed Lesia Tsurenko of Ukraine, who advanced without hitting a ball when high-profile Russian wild card Maria Sharapova withdrew due to an arm injury.
(Reporting by Larry Fine in Safety Harbor, Florida; Editing by John O'Brien)
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