Sloane Stephens powered into the WTA Mexican Open second round, while Victoria Azarenka disposed of Danielle Collins on Tuesday.
Stephens, the 2016 champion in Acapulco, needed just over an hour to brush past Pauline Parmentier 6-2 6-2 in her opener.
The American top seed and 2017 US Open champion was dominant, breaking three times in each set.
On the opposite side of the draw, Collins – the second seed and Australian Open semi-finalist – was no match for Azarenka.
The former world number one cruised past Collins 6-1 6-2 to set up a meeting with Tatjana Maria, who got past lucky loser Martina Trevisan 6-2 7-6 (7-1).
It was a relatively good day for the seeds at the WTA International event, with Johanna Konta, Mihaela Buzarnescu and Zheng Saisai advancing.
Konta cruised past Laura Siegemund 6-3 6-2, Buzarnescu was too good for Daria Gavrilova 6-4 6-2 and Zheng batted to a 3-6 7-5 6-4 win over Renata Zarazua.
Fifth seed Sofia Kenin led Rebecca Peterson 4-3 when the Swede retired 30 minutes into their encounter.
There were also wins for Christina McHale, Timea Babos, Varvara Flink and Bianca Andreescu.
At the Oracle Challenger Series event at Indian Wells, Kristina Mladenovic and Madison Brengle made second-round exits as Wang Qiang, Kristyna Pliskova, Kaia Kanepi and Taylor Townsend advanced.