Three-time defending champion Williams had the match on her racquet before having to withstand a fightback from her 23-year-old rival and taking two hours and seven minutes to reach the third round.
"She just started playing better, the kind of tennis she's never played before," said Williams yesterday.
"I made a few mistakes and then I had to pull myself back together. I feel like I was just playing, but it's all right. I'm back now and I'm going."
Williams fired 13 aces and 36 winners with 43 unforced errors while McHale responded with seven aces and 26 winners against 31 unforced errors.
Asked if she took McHale too lightly, Williams replied, "I don't underestimate anyone."
Williams, whose back-to-back finals losses at the Australian Open and Indian Wells were her first since 2004, served for the match in the 10th game of the second set but netted a backhand to surrender a break.
"She definitely started fighting back," Williams said. "And she's clearly capable of playing great tennis."
McHale denied Williams on three break points to hold the first game of the final set but Williams broke in the third and smashed a backhand service return winner to break again in the seventh game.
Williams had to fight off two break points in the final game, saving one with her 12th ace and the other with a service winner, and she blasted her 13th ace on match point to finally advance.
Two-time Wimbledon winner Petra Kvitova reached the third round with a 6-1, 6-4 victory over 83rd-ranked American Irina Falconi.
"I served pretty well," the Czech eighth seed said. "She played better in the second set and that's what made it tougher. It's always a little bit tricky when it's someone you have never played before."
Kvitova next faces Russian 30th seed Ekaterina Makarova, who ousted Ukraine's Lesia Tsurenko 3-6, 6-4, 6-3.
British wildcard Heather Watson ousted US 20th seed Sloane Stephens 6-3, 6-0. She faces Belgium's Yanina Wickmayer in the third round.
Uzbek Denis Istomin rallied to beat Croatia's Borna Coric 4-6, 7-5, 7-5 to book a Saturday matchup with British second seed Andy Murray, who won their only two matches back in 2013.
Japanese sixth seed Kei Nishikori plays his second-round match against French qualifier Pierre-Hugues Herbert, who downed Czech Lukas Rosol 7-5, 6-4.
Japanese qualifier Tatsuma Ito beat Nicolas Mahut 7-6 (7/3), 6-2 to book a second-round match with another Frenchman, 16th seed Gael Monfils.
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
