French Open champion Garbine Muguruza got a fright from Kayla Day but outlasted the precocious American teenager 3-6 7-5 6-2 to reach the fourth round of the WTA event at Indian Wells in California on Sunday (Monday AEDT).
Muguruza will next play Ukrainian Elina Svitolina, who beat Australia's Daria Gavrilova 6-2 6-1 in their third round clash.
Gavrilova was the last remaining Australian in the singles draw at the $US7 million ($A9.3 million) tournament after Samantha Stosur was knocked out by Julia Goerges in round two.
Day took the first set from the seventh seed Muguruza and had two break point opportunities at 5-5 in the second but the 17-year-old was unable to hammer home her advantage.
"I started a bit off," Muguruza said. "My shots weren't there. The experience of keeping calm and fighting helped; it's no secret.
"I think I'm improving in general a lot of things, but I know that maybe two years ago, this match I wouldn't turn it around. I think that's experience."
Muguruza was impressed with Day, the US Open junior singles champion.
"She reminds me a little of me, when I was super motivated and playing very good," she said.
Day hoped to learn from her defeat.
"I was pretty upset after my match, because it didn't go the way I wanted it in the end but if you look at the big picture, I was able to push a top-10 player really far," she said.
On a day when three matches went to third-set tiebreaks, there ultimately were no big upsets, with Czech third seed Karolina Pliskova and Russian eighth seed Svetlana Kuznetzkova also winning.
And fifth seed Slovakian Dominica Cibulkova also advanced, if only barely, saving a match point in a 2-6 7-6 (7-5) 7-6 (7-4) win over left-handed Czech Kristyna Pliskova, whose 18 aces were not enough.
Pliskova also had 13 break opportunities in the third set alone, but converted only two.
In an even closer encounter, Swiss 15th seed Timea Bacsinszky survived four match points to beat Dutch 18th seed Kiki Bertens 6-3 5-7 7-6 (10-8).
Eleventh seed Johanna Konta was the highest ranked player to fall, the Briton edged 3-6 6-3 7-6 (7-1) by Carolina Garcia of France.
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