First, Collins upset second-seeded Ons Jabeur of Tunisia 6-3, 1-6, 6-3 in a second-round match that had been pushed back to Thursday due to rain. Then Collins blitzed Sloane Stephens 6-2, 6-2 in a match-up of unseeded U.S. players.
Collins, a Floridian who is retiring at the end of the season, captured the Miami Open championship last week.
Next up for Collins will be a match against 11th-seeded Elise Mertens of Belgium, who got past seventh-seeded Elina Svitolina of Ukraine 6-4, 6-1. Earlier on Thursday, Mertens defeated France's Varvara Gracheva 6-4, 3-6, 6-2.
The United States' Jessica Pegula cruised into the quarter-finals with a 6-2, 6-2 victory over Poland's Magda Linette.
In other third-round action, Belarus' Victoria Azarenka, the 12th seed, rallied past the United States' Taylor Townsend 6-7(5), 6-3, 6-4 to reach the quarters.
Third-seeded Maria Sakkari of Greece downed Australia's Astra Sharma 6-4, 6-1, and fourth-seeded Daria Kasatkina of Russia eliminated 15th-seeded Anhelina Kalinina of Ukraine 6-1, 6-4.
Ninth-seeded Veronika Kudermetova of Russia toppled fifth-seeded Beatriz Haddad Maia of Brazil 7-5, 6-1, and Romania's Jaqueline Cristian beat 10th-seeded Emma Navarro of the United States 6-3, 5-7, 6-1.
Stephens won her second-round match earlier Thursday, defeating 14th-seeded Leylah Fernandez of Canada 6-4, 6-4.
Copa Colsanitas
Home favorite Camila Osorio, the sixth seed, moved into the quarter-finals at Bogota, Colombia, with a 7-6(4), 6-4 victory over Romania's Anca Alexia Todoni.
Osorio overcame eight double faults in part by winning 45 percent of her return points. Todoni put just 48 percent of her first serves in play.
Second-seeded Tatjana Maria of Germany had to wait out a lengthy delay caused by a power failure to overtake Argentina's Julia Riera 2-6, 6-0, 6-2.
Top-seeded Marie Bouzkova of the Czech Republic defeated the United States' Hailey Baptiste 6-3, 6-4, and seventh-seeded Laura Siegemund of Germany came from behind to top Great Britain's Francesca Jones 6-7(4), 6-4, 6-2.