World number one Angelique Kerber edged through at the Monterrey Open, while defending champion Heather Watson did likewise.
Kerber, who is enduring a difficult year so far, overcame Italian veteran Francesca Schiavone 4-6 6-0 6-4 in the first round on Tuesday.
The German had lost three of her previous five matches against Schiavone and a repeat looked likely until she steadied, with one break in the third set enough to see her advance.
Watson, whose third and most recent title came at the WTA International event last year, was also challenged.
The Brit eventually got past Nina Stojanovic 6-2 6-7 (7-9) 6-4 in almost three hours.
Seeds Carla Suarez Navarro, Timea Babos, Ekaterina Makarova and Alize Cornet all advanced.
Suarez Navarro had few problems against Alison Van Uytvanck in a 6-2 6-4 win and Babos cruised past qualifier Lesley Kerkhove 6-1 6-3.
Makarova overcame Denisa Allertova 6-4 6-3 and Cornet was too good for Irina Khromacheva 6-1 6-4.
The only seed to fall was Christina McHale, the American going down to qualifier Tereza Martincova 3-6 7-5 6-4.
Kristie Ahn advanced with a 6-4 6-2 win over Jana Cepelova and fellow qualifier Nadia Podoroska beat Madison Brengle 7-5 0-6 6-3.
Mandy Minella booked her spot in the second round with a 7-6 (7-3) 6-3 success over Elitsa Kostova.