World number one Serena Williams remained on course for a third consecutive Madrid Open title with a 6-2, 6-3 win over Spain's Carla Suarez Navarro.
Williams was broken twice in her opening three service games, but Suarez Navarro was unable to consolidate the break and once the American moved ahead 4-2 she saw out the set comfortably.
More of the same was to come in the second set as Suarez Navarro held serve just once and, despite her serve being broken twice more, Williams went on to set up a meeting with fifth seed Petra Kvitova in the last eight.
“I played Carla on clay I think last year, but in Rome. I feel like she actually played really well today, she made me work for every point and it wasn't an easy win,” said Williams.
Kvitova was also a winner in straight sets as she overcame Czech compatriot Lucie Safarova 6-4, 6-3.
Second seed Li Na had a more difficult morning as she had to come from a set down to beat 16th seed Sloane Stephens 2-6, 6-3, 6-2.
The Australian Open champion had no answer to Stephens's power in the first set as she dropped her first set of the week.
However, she responded well as one break of serve was enough to take the match into a third set and the Chinese star quickly took control of the decider as she raced into a 4-0 lead before comfortably seeing out the match.
“I think she was hitting the ball like pretty heavy. Normally the girls play flatter, but she was playing pretty heavy and it was my first time playing against her so she caused me problems,” admitted Li.
“After the first set I had to tell myself to calm down. After that you can only look forward otherwise you won't find a way back.”
Next up for Li is a meeting with four-time Grand Slam champion Maria Sharapova or Australian Sam Stosur in the last eight.