Seeds Kristina Mladenovic, Lesia Tsurenko and Andrea Petkovic advanced to the second round of the WTA Abierto Mexicano Telcel.
French second seed Mladenovic opened proceedings with a 6-2 6-3 victory over Varvara Lepchenko on the hard courts in Mexico on Monday.
After losing in the third round in Dubai last week, Mladenovic needed a little over an hour to book a second-round showdown with Heather Watson, who outlasted Bethanie Mattek-Sands 7-5 6-3.
"It was difficult for me, too, because I arrived just two days ago from Dubai," Mladenovic said.
"I'm still a bit jetlagged and it's totally different conditions here, but I'm just very happy with the win."
Ukraine's seventh seed Tsurenko eased past Chloe Paquet 6-2 6-1.
Awaiting Tsurenko in the next round is either Julia Goerges or Kateryna Bondarenko.
As for eighth-seeded German Petkovic, she rallied to beat qualifier Jamie Loeb 2-6 6-1 6-3.
Elsewhere, Pauline Parmentier prevailed 7-5 6-7 (6-8) 6-2 against Nicole Gibbs, Shelby Rogers trumped Louisa Chirico 6-2 6-2 in an all-American affair, while Kirsten Flipkens outlasted Renata Zarazua 7-5 6-7 (1-7) 6-1.