"We've played many times and it's always super-tough, super-exciting", said former world No.1 Muguruza.
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. She emerged for the second set but it was short lived.
Ranked 36th in the world, Williams endured three sets in her first two matches. "It's really a weird feeling, because I don't feel like I won the match point and (got the) "well done, ... good match". I will focus on getting better and start preparing for Miami".
Her opponent, 25-year-old Muguruza, noticed that something was awry with Williams too.
"Before the match I did not feel great, and then it just got worse with every second", Williams said afterward (via WTA Insider).
Williams, who made the semifinals in the desert past year, was playing McHale for the first time. In the victory, Venus won 59 percent of her first serve points and 52 percent of her second serve points.
Williams, who is now ranked number 10 in the world, has battled health issues in the past that nearly sidelined her ranking.
"When I was leading the match, she played without fear, I felt like she was playing much better in those games", Halep said.
"It was hard for me to close out those sets", Halep told reporters, praising Kozlova.
The Romanian was one of six seeds to progress, with Svitolina joining her after a 7-5 6-4 win over Daria Gavrilova.
Two seeded women lost: No. 11 Anastasija Sevastova, who retired trailing 5-0 in the first set against No. 21 Anett Kontaveit, and No. 15 Julia Goerges, who lost to Mona Barthel 7-5, 1-6, 6-4.