US Open champion Stephens advanced in Acapulco thanks to a 5-7 7-6 (8-6) 6-0 victory over Dutch qualifier Arantxa Rus.
Stephens, the winner of the WTA International tournament in 2016, claimed her first victory since winning last year's US Open on Wednesday (AEDT).
But she was forced to dig deep midweek, saving a match point in the second-set tie-break to prevail after two hours, 26 minutes.
Next up for Stephens is Stefanie Voegele, who defeated Maria Sakkari 6-3 6-3.
Tsurenko's title defence remains on track after she eliminated Australian Arina Rodionova 6-3 6-1.
The No.7 seed, from Ukraine, will face Kristina Mladenovic in the quarter-finals.
Frenchwoman Mladenovic, the No.2 seed, outlasted Beatriz Haddad Maia 3-6 6-3 7-5.
No.3 seed Daria Gavrilova survived a slight scare to overcome wildcard Renata Zarazua 7-5 6-3, with Veronica Cepede Royg awaiting the Australian in the next round.
Royg was too good for No.5 seed Irina-Camelia Begu 7-6 (7-3) 6-1, Monica Puig lost 6-1 6-4 to Rebecca Peterson, while Zhang Shuai saw off Jil Teichmann 7-6 (7-5) 6-4.