Stephens saved five set points in the opening set Wednesday and beat No. 23 Petra Cetkovska 7-6 (6), 4-6, 6-3.
"I'm 19 and I do still have some lapses," Stephens said. "They're less now than I used to have in the past. I really don't get as upset when I lose points now. I'm not that emotional anymore."
In the final set, she trailed love-30 in four consecutive service games, yet won them all.
"I don't know what was going on," Stephens said. "It was ridiculous, but then I served great the rest of the game."
Ranked 59th, Stephens is playing at Wimbledon for the first time. She's coming off her first run to the fourth round at a Grand Slam tournament, which came this month at the French Open.
"It takes time to build your concentration and focus," she said. "It has gotten better and better with time, and I think playing better players helps."
Stephens, the daughter of a former NFL star and a college All-American swimmer, said some of her confidence comes from feeling she belongs on the tour. She has forged friendships with many players, including 13-time Grand Slam champion Serena Williams.
During the Fed Cup tie against the Ukraine in April, Stephens and Williams hung out together at the Kharkiv resort where they were staying. They even enjoyed bonding adventures such as driving a golf cart around a course in the dark.
"That's my girl," Stephens said of Williams. "She's so goofy. We're just friends, we get along well. We click. About everything we talk about we agree.
"She's funny and we're always laughing. We can't be serious. People don't really see who she is because they only see what she is on court. But who cares? Her friends know who she is."
Stephens faces No. 15 Sabine Lisicki in the third round.
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