Third seed Petra Kvitova is safely into the third round of the 2019 Miami Masters after a straight sets win over Greece's Maria Sakkari on Thursday.
Venus Williams is into the second round, as she maintained her good form to see off the challenge of Dalila Jakupovic.
Indian Wells champion Bianca Andreescu survived a stiff test in her first-round encounter with Romania's Irina-Camelia Begu.
The 18-year-old saved a match point in the second set, before coming back to win in three and move into the second round.
On the men's side of the draw, there was disappointment for Great Britain's Cameron Norrie, who was beaten in three sets by Jordan Thompson.
Elsewhere, Albert Ramos Vinolas, Bernard Tomic and Feliciano Lopez all secured victories on Thursday.
Women's Early Results
Venus Williams def. Dalila Jakupovic 7-5, 6-3
Taylor Townsend def. Johanna Larsson 6-1, 6-2
Whitney Osuigwe def. Mari Osaka 6-2, 6-4
Xin Yu Wang def. Misaki Doi 2-6, 6-1, 6-3
Alison Riske def. Kaia Kanepi 6-2, 6-2
Yanina Wickmayer def. Sachia Vickery 3-6, 6-3, 6-1
Petra Kvitova def. Maria Sakkari 6-1, 6-4
Yafan Wang def. Kristina Mladenovic 6-3, 6-3
Viktoria Kuzmova def. Daria Gavrilova 6-4, 6-2
Rebecca Peterson def. Laura Siegemund 6-1, 5-7, 7-5
Bianca Andreescu def. Irina-Camelia Begu 4-6, 7-6 (2), 6-2
Men's Early Results
Bernard Tomic def. Thiago Monteiro 6-4, 6-1
Maximilian Marterer def. Taylor Fritz 6-4, 3-6, 6-3
Damir Dzumhur def. Christopher Eubanks 1-6, 6-4, 7-6 (5)
Lorenzo Sonego def. Martin Klizan 6-4, 6-3
Dusan Lajovic def. Pablo Cuevas 6-4, 6-7 (6), 6-3
Alexander Bublik def. Tennys Sandgren 5-7, 6-4, 7-6 (5)
Jordan Thompson def. Cameron Norrie 4-6, 7-6 (5), 6-3
Leonardo Mayer def. Mikael Ymer 4-6, 6-3, 6-4
Robin Haase def. Lukas Lacko 6-2, 6-4
Felix Auger Aliassime def. Casper Ruud 3-6, 6-1, 6-2
Albert Ramos Vinolas def. Marius Copil 6-4, 6-2
Nicolas Jarry def. Jeremy Chardy 6-7(1), 6-2, 7-6 (5)
Radu Albot def. Matthew Ebden 6-0, 3-2 (retired)
Feliciano Lopez def. Benoit Paire 7-5, 4-6, 6-4
Full results and schedule are available from the tournament's official website.
Kvitova was made to work hard against Sakkari but came through to win the second-round match in an hour and 10 minutes.
The No. 3 seed started strong and quickly moved into a 3-0 lead, with Sakkari struggling with her serve initially.
Kvitova managed to seal a double break to move 5-1 up and had no problems at all serving it out to take the first set comfortably:
However, Sakkari hit back and showed her quality at the start of the second. She went on the attack against Kvitova's serve and was rewarded with an early break to go 2-0 up.
Yet Kvitova quickly reeled her back in, winning four consecutive games to take charge of the match.
Sakkari managed to save a match point at 5-3, leaving Kvitova to serve out the victory:
Andreescu had a far tougher test as she produced a memorable comeback to knock out Begu.
The teenager was second best in the opening stages against a sharp Begu who served well, took her opportunities and produced some impressive groundstrokes.
The second set was a rollercoaster affair with the players trading breaks in the opening stages before Begu moved into a 5-1 lead and looked set to coast to victory.
However, Andreescu then produced her very best tennis to win five games in a row and move 6-5 ahead:
Begu managed to force the tie-break, but the teenager once again demonstrated her brilliant shot-making to take the set and force a decider.
The momentum was with Andreescu in the third set, and she dropped just four points on serve on her way to a dramatic win in two hours and 33 minutes:
Andreescu goes on to play No. 32 seed Sofia Kenin next. The American is the last player to beat her, having won in three sets in the semi-finals in Acapulco in February.