Top seed Serena Williams came from a set down to book her place in the Stanford Classic semi-finals with a hard-earned 2-6 6-3 7-5 win against fifth-seeded Serb Ana Ivanovic.
Serena, whose sister Venus was beaten in three sets by Germany's Andrea Petkovic earlier in the day, initially struggled on a fast playing surface but gradually found her range to seal victory in just under two hours.
Ana plays very well. This surface was a little fast so she was hitting a lot of shots.
"It wasn't very easy," Serena, who will face Petkovic in the last four on Saturday, told reporters. "Ana plays very well. This surface was a little fast so she was hitting a lot of shots."
Serena was broken in the first game of the match, then double-faulted to lose serve again in the fifth and trail 1-4 before losing the opening set in just under 30 minutes.
However, the American used her crunching ground strokes to great effect in the next two sets and, helped by 10 aces, she wrapped up the win when her opponent sent a forehand service return wide.
Venus crashes out
Earlier, the eighth-seeded Petkovic battled past Venus Williams 6-1 3-6 7-5 in a pulsating match lasting nearly two hours.
Former world number one Venus, who had upset fourth seed Victoria Azarenka in straight sets in the previous round, fought back from 6-1 and 2-0 down to level the match but the German regained control in the decisive third set.
In the other two quarter-finals, third-seeded German Angelique Kerber swept aside Spaniard Garbine Muguruza Blanco 6-2 6-1 while Varvara Lepchenko crushed fellow American Sachia Vickery 6-1 6-0.