With sweltering temperatures reaching a Wimbledon record 35.7C, five-time champion Williams kept her cool to dispatch world number 93 Babos with 12 aces and 23 winners in just 59 minutes on Centre Court.
The 33-year-old, bidding for a third Grand Slam title of the year, will play Britain's Heather Watson for a place in the last 16.
"I'm definitely playing well, which I never say, but I had two really tough matches straight off the bat so I had to pick up my game," Serena said.
"I really had no option but to play well so far. But I'd like to believe I have a lot of room to improve."
Williams has swept to Australian and French Open triumphs over the last six months, taking her within two major titles of becoming the first woman since Steffi Graf in 1988 to claim the four top titles in one year.
The American great also won the US Open to end 2014 on a high and is heavy favourite to continue that dominant run by taking the Wimbledon title for the sixth time in her illustrious career.
Her failure to make the All England Club quarter-finals for the last two years led Serena to caution against labelling her as a certainty to become the first woman to win the French Open and Wimbledon back to back since she achieved the feat in 2002.
But, on this evidence, she is approaching peak form at just the right time.
That resounding statement of intent was enough to seal the first set and she raced through the second in even quicker time to complete a comfortable stroll.
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
