Stephens, whose best result this year was a run to the Madrid semi-finals in May, was misfiring from the start and never managed to settle into much of a groove in her first meeting with the Swedish world number 70.
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Peterson enjoyed a dream start as she raced out to a 5-2 lead and ultimately took the opening set in 29 minutes when Stephens sent a routine backhand from the baseline into the net.
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Stephens, who triumphed here in 2015, started to settle down in the second and led 5-4 but Peterson broke back to get back on serve and never looked back.

Rebecca Peterson of Sweden reacts to winning match point against Sloane Stephens of the United States during Day 2 of the Citi Open at Rock Creek Tennis Center on July 30, 2019 in Washington, DC

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Up next for Peterson will be Italian Camila Giorgi, who defeated Sachia Vickery to advance.
Gauff, the 15-year-old sensation who made a stunning run to the fourth round at Wimbledon and came through qualifiers to reach the main draw in Washington, fell 6-4 6-2 in the afternoon to Zarina Diyas of Kazakhstan.
The turning point came at the end of the first set as Diyas converted her fourth set point of the game when Gauff sent a forehand into the net.

Cori Gauff of the United States reacts during her match against Zarina Diyas of Kazakhstan during Day 2 of the Citi Open at Rock Creek Tennis Center on July 30, 2019 in Washington, DC

Image credit: Getty Images

That brought an end to a game that had lasted more than 10 minutes and left the youngster visibly frustrated.
Diyas held at love to start the second set and rolled to the win before packed stands on a hot and humid day in the U.S. capital.
Gauff did herself no favours, smacking her 33rd unforced error on match point having also given Diyas 16 break points, five of which she was able to convert.
As one American teenager faltered another delivered as unheralded 17-year-old Hailey Baptiste shocked second-seeded Madison Keys 7-6(4) 6-2 in their first-round meeting.
Keys appeared in control when she went up a break in the first set but Baptiste immediately broke back and managed to out-slug the hard-hitting Keys the rest of the way to claim her first career WTA match win.
Olympic champion Monica Puig, fourth seed Hsieh Su-wei and France's Kristina Mladenovic all advanced in straight sets to the second round on Tuesday.
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