She is now ranked 10th in the world and was playing in her first tournament since the Australian Open in January.
"We've played many times and it is always super tough and super exciting".
Williams made a solid start to Sunday's contest in California as she raced into a 3-0 lead, dominating from the baseline with a string of powerful forehands.
"Before the match, I did not feel great, and then it just got worse with every second; extreme dizziness and extreme fatigue", Williams said in a statement posted by the tournament.
Venus Williams is coming off a straight sets win over Christina McHale that took 20 games to decide.
"I wish I'm going to see her soon and feeling better", added the Spaniard, who advanced to a fourth-round clash with seventh-seeded Kiki Bertens of the Netherlands, a 7-6 (12/10), 6-4 victor over Britain's Johanna Konta.
"By the score, it might have looked like I started well, but I was not feeling at all well physically", Williams said.
"It's really a weird feeling, because I don't feel like I won the match point and [heard], 'Well done, good match, '" she said.
"I had to adapt a little bit my position in the court, the way I was hitting, and it took me a few games to kind of do it", Muguruza said. Barthel has a chance to win four matches in a single tournament for the first time since a challenger tournament in Chicago back in September.
"It was hard for me to close out those sets", Halep told reporters, praising Kozlova. The next was the 2016 French final, where Murguruza won 7-5, 6-4.
The result saw Muguruza set up a fourth-round meeting with Kiki Bertens, the seventh seed who overcame Konta 7-6 (12-10) 6-4.