Lesia Tsurenko made a winning start to her title defence at the Abierto Mexicano Telcel, while third seed Daria Gavrilova was also victorious on day one.
Defending champion Tsurenko was a 6-4 6-1 winner against American Lauren Davis in Acapulco on Monday.
Davis was involved in a marathon encounter with eventual runner-up Simona Halep at the Australian Open, where she helped equal the tournament women's record for most games played in a third-round epic at Melbourne Park.
But Davis was no match for Ukraine's Tsurenko, who will meet Australian Arina Rodionova after Kateryna Kozlova was forced to retire from the match trailing 6-2 1-0.
Another Australian, Gavrilova, was forced to dig deep as she prevailed 4-6 6-3 6-3 against Madison Brengle.
Gavrilova struggled on serve but still managed to progress after two hours, 21 minutes at the WTA International event.
"It was so hot, especially in the first set, but I looked at the weather forecast and so I knew it that after an hour or so the weather would drop down," Gavrilova said.
"I was just trying to hang in there for the first set and trying to be really tough battling it out. And when the weather went down I felt much better."
Elsewhere, fifth seed Irina-Camelia Begu overcame Christina McHale 3-6 6-2 6-4, Veronica Cepede Royd rallied past Belinda Bencic 4-6 7-6 (7-1) 6-3, while Monica Puig made it through after Dayana Yastremska retired when she was down 2-6 6-4 5-0.Published 27 Feb 2018, 10:35 IST