Williams was back in action in only her fourth
tournament of the season and the first since being forced to
withdraw from the Miami Open in March due to a knee injury.
The 37-year-old American fell behind 3-1 but recovered with a
string of powerful groundstrokes from the baseline, clinching
five of the next six games for the opening set.
Peterson, the world number 64, dug deep to grab two break points
in the final game of the match but Williams saved both, before
wrapping up the win in an hour and 15 minutes.
Williams, a 23-times Grand Slam singles champion, has finished
runner-up at two of the last three majors but been unable to add
to her tally since returning to the sport following the birth of
her first child in 2017.
Williams, who has dropped to number 11 in the world rankings,
will next face the winner of the first round clash between her
sister Venus and reigning Qatar Open champion Elise Mertens.
After an opening round exit at the Madrid Open last week, former
world number one Garbine Muguruza scored her first win in over a
month as she eased past China's Zheng Saisai 6-3 6-4.
(Reporting by Hardik Vyas in Bengaluru; Editing by Ian Chadband)
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