Maria Sharapova was pleased with her win against Timea Babos - and says she went into the decider feeling confident in her ability to pull off an impressive comeback.
Sharapova is playing in her first Grand Slam tournament since serving a 15-month doping suspension.
Sharapova was also able to better dictate the pace of the match from the baseline, especially with her forehand. "She played consistently much better than I did".
"When the draw came out I knew what a hard matchup this would be, how much excitement was behind this matchup and the hype", she said. "I would have needed a round or two to get things started again".
"This girl has a lot of grit and she's not going anywhere", Sharapova told the crowd in an on-court interview.
Kuznetsova's entry to the second round required a bit more work, as she staved off three match points to defeat Marketa Vondrousova 4-6, 6-4, 7-6 (2).
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Williams, the No. 9 seed, plays Oceane Dodin of France at night.
Despite seeing a backhand volley clip the net cord twice before dropping her side, Sharapova held in a tense sixth game and converted break point at the third time of asking in the next to force a decider.
Svitolina breezed through the first set before posting a 6-0, 6-7 (5), 6-3 victory over Siniakova, the world's 42nd-ranked player.
Snubbed by the French Open and then injured for Wimbledon, where she would have had to fight her way through qualifying, Sharapova was controversially given a wild card in NY.
She also had a sleeve on her right elbow to keep that arm warm, she said.
The 2006 champion fired 12 aces with 39 winners and 36 unforced errors.
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Assuming her 6-foot 2-inch frame can recover from Monday's classic, the more powerful Sharapova should have the upper hand against the shorter 24-year-old from Hungary.
In her remarkable victory on the opening day over the world No 2, Simona Halep, the support for Sharapova in Arthur Ashe Stadium was overwhelming.
She is branded and nothing Maria Sharapova does on the tennis court for the rest of her career will erase the scarlet letter "M" (for Meldonium, not Maria) that she wears on her custom-designed outfits. Babos reacted with a loud yell.
It appeared to be a case of "after the lord mayor's show" as she lost the first set but her battling qualities were back on show to eventually take her through to round three, where she will face American wildcard Sofia Kenin.
No. 19 Anastasia Pavlyuchenkova missed her opportunities Wednesday, as she fell 3-6, 6-3, 6-2 to Christina McHale of the U.S. In other matches, No. 10 seed Agnieszka Radwanska of Poland beat Petra Martic 6-4, 7-6 (3), and Vandeweghe beat fellow American Alison Riske 2-6, 6-3, 6-4.
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