Mattek-Sands eliminated seventh-seeded Tamira Paszek 6-2, 6-4. Mattek-Sands landed just 38 percent of her first serves but still took two-thirds of the points while serving.
She had her serve broken once but countered that with a pair of breaks in each set.
No. 5-seeded Julia Goerges also advanced, beating Daniela Hantuchova 6-5, 7-6 (7-5). Goerges only saw one break point in the match.
Qualifiers Mallory Burdette and Kirsten Flipkens joined Mattek-Sands in the second round. Burdette piled up six breaks in beating Ksenia Pervak 6-3, 6-4 while Flipkens was a 6-4, 6-3 winner over Alize Cornet.
Romina Oprandi had the easiest match on Tuesday's schedule, racing past Alexandra Cadantu 6-2, 6-1 in 55 minutes. Oprandi lost only 14 points over eight service games and saved all three break points Cadantu managed.
Also Tuesday, Irina-Camelia Begu topped Catalina Castano 6-0, 6-4; Carla Suarez Navarro defeated Magdalena Rybarikova 6-3, 6-4; Andrea Petkovic got by Barbora Zahlavova Strycova 7-6 (7-3), 6-2; and Simona Halep was up 3-0 when Lesia Tsurenko retired with a right shoulder injury.