World number 26 Camila Giorgi battled from a break down in both sets to beat fifth seed Muguruza 7-5 6-3 in an hour and 53 minutes.
That meant 12th seed Giorgi made her second straight quarter-final, after a last-eight appearance in Birmingham, and will next face Viktoriya Tomova, who defeated Kirsten Flipkens 3-6 6-3 6-4.
Jil Teichmann, the 10th seed at the tournament, was a notable second-round elimination, falling to a 7-6 (9-7) 4-6 6-3 defeat to Briton Harriet Dart, who later triumphed 6-4 2-6 6-4 over Marta Kostyuk.
Dart's fellow Briton Katie Boulter stunned last year's Wimbledon runner-up Karolina Pliskova in the second round but had no such luck against Petra Kvitova, losing 5-7 6-0 7-5.
Beatriz Haddad Maia, the winner at the Birmingham Open last week, extended to a 12-match winning streak with a 6-1 6-2 victory over Jodie Burrage.
Jelena Ostapenko also progressed after Madison Keys retired when 6-3 down and will next face Anhelina Kalinina, who battled to a 6-3 2-6 6-3 win over 16th seed Yulia Putintseva.
While seeds fell at Eastbourne, there were not as many shocks at the Bad Homburg Open, where Angelique Kerber defeated Lucia Bronzetti 6-2 6-3 to reach the quarter-finals.
Fourth seed Simona Halep also made the last eight with 6-0 6-3 victory over Tamara Zidansek and will meet Amanda Anisimova after she won an All-American match against Ann Li 6-0 6-2.
Alize Cornet downed Tatjana Maria 7-6 (7-4) 6-4 to tee up a clash with Kerber, while Bianca Andreescu will meet top seed Daria Kasatkina after defeating Katie Swan 6-4 6-4.