Second seed Ash Barty fought off a stiff challenge at the end of the second set to beat American Lauren Davis 6-2 7-6(2) and reach the third round of the U.S. Open on Wednesday. The French Open champion came to the net to great effect, proving the more aggressive player as she used her slice to dictate the pace of the contest and fired 35 winners, 22 more than her opponent. "There were parts of my game that I still want to clean up," Barty said after the match. "I had to hit a lot of balls tonight, it was extremely tough." Davis mounted a fierce defensive effort, saving 14 of 18 break points the Australian earned, and had a set point herself at 5-4 in the second stanza at Louis Armstrong Stadium. But she was not immune to the intense pressure of the match, kicking a tennis ball into the stands in frustration after knocking it into the net at 5-6 in the second set to give Barty the advantage. Barty ultimately battled through to a tiebreak and secured the victory when the American went wide with a forehand at the end of another lengthy rally. Avoiding a third set was a bonus for Barty, who would have been looking to conserve as much energy as possible for a campaign she hopes will go deep into the second week. Next up for the world number two is a meeting with either Maria Sakkari of Greece or China's Peng Shuai on Friday, when victory would take her into the fourth round at Flushing Meadows for only the second time. "There's always room for improvement every single match that you play," said Barty. "I think that's the beauty of this sport: now that I'm still alive in the tournament, I get an opportunity to do that in my next round."