Top seeds Ana Ivanovic and Sara Errani progressed to the Monterrey Open quarter-finals, while eighth seed Magdalena Rybarikova saved match points in her win.
Ivanovic beat Pauline Parmentier 6-3 6-2 at the WTA International event in Mexico, the defending champion moving to a 3-0 head-to-head record against the Frenchwoman.
The Serb, ranked sixth, saved all four break points she faced, while effecting three of eight on the Parmentier serve to advance in one hour, six minutes.
Earlier, Errani - the second seed - was too good for qualifier Timea Babos at the hard-court event, 6-3 6-3.
It was no easy contest for the Italian despite the straight-sets scoreline, as Errani faced 12 break points - saving nine of them.
Babos, though, was much less clinical under pressure, losing serve six times as the Hungarian's tournament ended.
Slovakia's Rybarikova saved four match points on her way to beating Polona Hercog 7-5 3-6 7-6 (11-9) in two hours, 46 minutes.
Hercog, of Slovenia, was one point from a quarter-final berth on four occasions - twice on her own serve - in the deciding tie-break, but Rybarikova denied her.
The eighth seed needed only one match point of her own to progress, and she will take on one of either Caroline Garcia or Francesca Schiavone next.
Frenchwoman Kristina Mladenovic defeated Vera Zvonareva 6-4 6-2 in one hour, 24 minutes.
Mladenovic hit eight aces on her way past the former world number two, to reach the last eight of an International-level tournament for the first time since July.