Lepchenko started slowly in the first set, falling 6-1. She rebounded strongly, taking the second and third sets, 6-3 and 6-4 respectively, to advance.
The 29-year-old Allentown resident will play 20th-seeded Victoria Azarenka in Monday's fourth round.
"I just kept on fighting, fighting, fighting, fighting, fighting, fighting — and I won," Lepchenko said during an on-court interview immediately after her victory. This is the first time in six US Open appearances that Lepchenko has advanced past the third round.
The key game of the match came in the third set with Lepchenko serving but trailing Barthel, 4-3.
Lepchenko showed some frustration — slamming her racket into the net and throwing her hands into the air — after failing to execute on several points, but she overcame those mistakes and fought off a couple of game points to even the set at 4.
On serve, Lepchenko broke Barthel to take the 5-4 advantage then closed out the decisive set, and the match, to the delight of the crowd.
"You were amazing today," Lepchenko said to the fans inside Louis Armstrong Stadium. "I wouldn't have been able to do it without you. You guys kept on cheering for me."
Lepchenko said she drew on the experience of playing Barthel at last month's Bank of West Classic on the campus of Stanford University. In that quarterfinal-round match, Lepchenko dropped the first set before rallying to win the final two.
"I tried to do the same thing that I did in Stanford," she said. "I worked at staying aggressive and doing what I had to do to pull it out."
Next up for Lepchenko, ranked 46th in the world, is her first match of this US Open against a seeded opponent.
In Azarenka, Lepchenko faces a foe coming off an exciting three-set third-round victory over 11th-seeded Angelique Kerber, 7-5, 2-6, 6-4. Azarenka leads the head-to-head against Lepchenko, 3-1.
Lepchenko made it through to the round of 16 with back-to-back-to-back wins over Kirsten Flipkens 6-1, 6-1; Lesia Tsurenko 7-6 (9-7), 6-2; and the three-setter over Barthel.
After Saturday's triumph, Lepchenko was asked about becoming an American citizen and if the US Open felt like her home tournament.
Lepchenko was born in Uzbekistan. She became a U.S. citizen in September 2013.
"Yeah, I've practiced here [USTA Billie Jean King National Tennis Center] for so many years, since 2011," she said. "And I've been living in the U.S. since I was 15 so even though it happened two years ago, I've felt like an American all along."
Michael Blouse is a freelance writer.