The two-time Australian Open champion, now ranked 37 in the world, triumphed 6-4 6-2 to set up a clash with top seed Paula Badosa at the Centro Panamericano de Tenis in Mexico.
Alize Cornet of France surrendered a lead to lose 3-6 6-3 6-4 to China's Lin Zhu but world number 22 Liudmila Samsonova beat Kaia Kanepi 6-1 7-5.
Meanwhile, former US Open winner Bianca Andreescu needed just 80 minutes to dispatch Switzerland's Jil Teichmann 6-2, 6-4.
"I definitely like the atmosphere here. I think the altitude helps me in a way, especially when I'm hitting winners," said Andreescu, who is making her first appearance at this event. "I feel like it just drags [the ball] around, which I actually like. I just wanted to come out, stay positive and give everything I have.
"I'm very happy with the consistency. Sometimes, I could've went for more, but I chose to be a little bit more safe. I didn't want to go for too much ... there's a good balance. I think my serve went really well today, my return, and just fighting until the end, as well."
Andreescu moves on to face another former Grand Slam winner, two-time Wimbledon champion Petra Kvitova, who also advanced late in the day after seeing off Bernarda Pera 6-3, 7-5.
American Sloane Stephens, Belgian Elise Mertens, Ukrainian Marta Kostyuk and Canadian Rebecca Marino all advanced to the second round as well after straight-sets wins.