Sharapova hit 25 unforced errors in the opening set and was in uncharacterisitic form against the 18-year-old American.
But she was let off the hook by the inexperienced youngster – who struggled with her own service game – and went onto win the match in straight sets (7-5, 6-2) at Flushing Meadows.
Kenin did put up a fight though, and proved to be a tricky opponent for the five-time Grand Slam champion – who took 67 minutes to win the opening set.
But Sharapova is fully aware that she must improve ahead of her fourth-round clash with 16th-seed Anastasija Sevastova if she has any chance of progressing to the quarter-finals.
The former world No. 1 also heaped praise on Kenin for her gritty performance, but was relieved to get herself over the line.
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“We’ve never faced off against each other, she’s up and coming and she’s got to the third round of the US Open,” Sharapova said.
“She came out and had nothing to lose today and that’s always dangerous, so I’m really glad that I got through.
“I didn’t see the ball too well in the beginning of the match and made a lot of unforced errors as I was moving forward – but I wasn’t getting the shots that I wanted.
“But ultimately I won the last point and I’ve got a chance to go to the practice court tomorrow and work on it a little bit, regroup and start over again the next day.”
Prior to her win over Kenin, the 2006 US Open champion beat Simona Halep and Timea Babos.