The 21-year-old Gavrilova earned her first victory over a top-10 player with a 7-6 (7-4), 6-3 decision in Thursday's second-round action.
Gavrilova, who is playing in her first Miami Open, will face Kurumi Nara of Japan in the third round. Nara got past No. 25 seed Caroline Garcia 6-3, 7-6 (11-9).
Former world No. 1 Caroline Wozniacki did move on, routing American Madison Brengle 6-0, 6-1 in 56 minutes on the hardcourts at Crandon Park. The fourth- seeded 2014 U.S. Open runner-up Wozniacki will next face Estonia's Kaia Kanepi, who doused 28th-seeded American Varvara Lepchenko 6-2, 6-4.
Venus Williams began her 16th appearance at the Miami Open by beating Polish qualifier Urszula Radwanska by a 6-3, 6-2 margin. It was Williams' first match since the semifinals at Doha in late February.
Williams, seeded 16th, won the title here in 1998, 1999 and 2001. Next up for Williams is No. 23 seed Samantha Stosur, who outlasted French qualifier Pauline Parmentier 6-1, 3-6, 6-0.
Meanwhile, seventh-seeded 2012 Miami champ Agnieszka Radwanska handled Slovak Anna Schmiedlova 6-4, 7-5, eighth-seeded Russian left-hander Ekaterina Makarova mauled Italian Karin Knapp 6-1, 6-3 and ninth-seeded German Andrea Petkovic rolled past American Christina McHale 6-2, 6-2.
Also, 12th-seeded Spaniard Carla Suarez Navarro handled Swiss Stefanie Voegele 6-3, 6-1 and 14th-seeded rising Czech star Karolina Pliskova overcame German Annika Beck 2-6, 6-3, 6-4.
Little-known Spaniard Paula Badosa Gibert ousted lucky loser Zheng Saisai 6-1, 7-5.
In other action involving seeds, France's Kristina Mladenovic took out No. 19 Czech Barbora Zahlavova Strycova 7-5, 6-2; No. 22 Frenchwoman Alize Cornet eliminated Russian Elena Vesnina 6-4, 6-1; No. 26 Elina Svitolina beat Bojana Jovanovski 6-3, 7-6 (7-3) and No. 31 Romanian Irina-Camelia Begu overcame Czech Tereza Smitkova 5-7, 6-4, 6-4.
The 2015 Miami champion will earn $900,400.