Defending champion Timea Babos was among those in action on Day 1, winning her opener in straights.
Former Top 15 player Eleni Daniilidou wasn't so lucky, falling in three sets to Galina Voskoboeva.
Marion Bartoli looked headed for victory against Coco Vandeweghe on Day 2, up by a set and a break.
But Vandeweghe's serve was just too strong - she hit 11 aces to defeat Bartoli in three, 46 63 61.
Serbian qualifier Jovana Jaksic battled for over three hours to beat Vera Dushevina, 46 76(4) 76(2).
Maria Kirilenko won 10 straight points from 5-all to take control of Ximena Hermoso and win, 75 61.
Urszula Radwanska put the trademark Radwanska squat shot on display to beat Donna Vekic on Day 3.
Also advancing on Day 3 was Anastasia Pavlyuchenkova, who stopped Croatian qualifier Tereza Mrdeza.
Bartoli wasn't the only big early upset - Ana Ivanovic also got picked off in the early rounds.
But the former No.1's loss came to someone who knows her way around Monterrey - the 2012 champion.
The last three quarterfinal spots were up for grabs on Thursday, including an all-American duel.
It was Lauren Davis who came up a winner in that one, edging Vandeweghe in a tight one, 64 76(8).
Kirilenko started well in her match but said afterwards she may have lost concentration mid-way.
Jaksic, the marathon winner over Dushevina from earlier in the tournament, won the second set.
But Kirilenko rebounded in the third to prevail, 60 46 61, as second round action came to a close.