Sloane Stephens finally ended her long wait for another win, while Kristina Mladenovic also progressed at the Mexican Open on Tuesday.
Stephens, the 2016 champion in Acapulco, claimed her first victory since winning the US Open last year.
The American top seed eased past Pauline Parmentier 6-4 6-0 in the first round of the WTA International event.
Stephens will next face qualifier Arantxa Rus, who overcame teenager Kayla Day 4-6 6-1 6-0.
Another player who endured a miserable finish to last year, Mladenovic, also cruised through.
The second seed, last year's runner-up, was untroubled by qualifier Amandine Hesse in a 6-2 6-2 victory.
Awaiting Mladenovic in the second round is Beatriz Haddad Maia, who beat Heather Watson 7-5 4-6 6-1.
Another seed to progress was Zhang Shuai after she needed just 54 minutes to crush Jasmine Paolini 6-3 6-1.
There were just two seeds to fall as Alize Cornet and Tatjana Maria exited.
Cornet fell to qualifier Rebecca Peterson 6-2 6-4 and Maria was downed by Stefanie Voegele 6-2 7-5.
Maria Sakkari overcame Lara Arruabarrena 6-3 7-6 (7-1), Renata Zarazua was too good for Kristyna Pliskova 6-3 6-4 and Jil Teichmann battled past Jana Fett 7-5 7-5.