Sharapova, who made her competitive comeback in April after a 15-month ban following a positive test for meldonium, battled through the first two rounds and it seemed that she would also struggle against the 18-year-old Kenin.
Hitting winners and unforced errors in almost equal measure in the opening set, the former world number one however, dug deep to take the advantage.
Kenin's tank was empty in the second set and Sharapova, who next faces Latvian 16th seed Anastasija Sevastova, opened up a 3-0 lead and ended the contest on the first match point when the American sent a backhand wide.
"We had never faced each other and she came out having nothing to lose and it's always dangerous so I'm happy I went through," said Sharapova, who won her only U.S. Open title in 2006.
Sporting a leather-collared black dress encrusted with crystal, Sharapova made a rock star entrance on a packed Arthur Ashe Stadium to close the night session.
However, she made nine unforced errors in the first three games, which continued throughout the first set but she broke in the 12th game when Kenin could not retrieve a powerful flat forehand and she then raced through the second set.
It was a relief for Sharapova after she had to endure two three-set matches to reach the third round.
"Coming into this match playing two three-setters, I'm just happy I got it done in two. Give my body a little bit of a break," she said.
"I took a day off yesterday just as a prevention.
"I did not see the ball too well at the beginning of the match, I wasn't getting the shots that I wanted ... but got better as the match went on."
(Editing by Greg Stutchbury)
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