The American, who rolled her right ankle in her first match, rebounded on Thursday with a crushing 6-2 6-0 win over Spanish teen Garbine Muguruza.
Despite suffering the ankle problem in the first set of her opening clash, against Edina Gallovits-Hall, she went on to record a 6-0 6-0 victory.
She did not appear to be troubled by the issue on Thursday, kept under control by painkillers.
"I didn't feel anything today," Williams said after booking a date on Saturday with Japan's Ayumi Morita.
"Obviously when you go out to play, you're heavy on adrenaline and you're really pumped up.
"Usually I feel injuries after the match but, so far, so good. I felt pretty much better than I ever dreamed of expecting to feel."
Williams said she was in some discomfort when she hit indoors on Wednesday and was surprised to wake up and find the pain had all but gone.
"I think she moved me more in the second set, so I was able to test it more.
"I was pretty confident. Like I said, I didn't feel any pain, so I was really confident with moving. I think the mental is the most important part."
Her only problem was hitting herself in the mouth with her racquet while completing a follow-through.
She bled from her upper lip but said: "It's okay. It's a war wound."
Meanwhile, defending champion Victoria Azarenka sent out a powerful warning to her rivals when she sailed into the third round.
The world No.1 said she was back in competitive mode following a near whitewash of Greek player Eleni Daniilidou.
Azarenka skipped through with a 6-1 6-0 victory which took her just 55 minutes to complete and next faces American Jamie Hampton.
"Today was much better," Azarenka said.
"I felt like I am back in the competitive mode in the tournament and more focused and that was the best part for me."
The world No.1 tore through the opening set in only 24 minutes but was helped when Daniilidou double-faulted twice while facing break points.
Former world No.1 Caroline Wozniacki made it through to the third round when she overcame Croatian Donna Vekic 6-1 6-4.
The Dane will play Ukrainian qualifier Lesia Tsurenko for a spot in the last 16.
Italian 16th seed Roberta Vinci also made light work of her second-round match, reaching the third round with a 6-3 6-2 win over Uzbekistan's Akgul Amanmuradova.
Russian 14th seed Maria Kirilenko scored a 7-5 6-2 win over China's Shuai Peng, while 42-year-old Kimiko Date-Krumm, the oldest winner of a women's singles match in history, marched on with a 6-2 7-5 second-round victory over Israeli Shahar Peer.