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Lisicki has always thrived at Wimbledon, enjoying a memorable run to the last four as a wild card last year and reaching the quarter-finals in 2009.
She enjoyed shock wins over top 10 seeds Li Na and Marion Bartoli at Wimbledon 12 months ago and will relish a likely revenge mission in the fourth round next week.
Lisicki, seeded 15th, will play world number one Maria Sharapova if the French Open champion defeats Taiwan's Hsieh Su-Wei later on Friday.
That would give the 22-year-old a chance to avenge her straight sets loss against Sharapova in last year's semi-finals.
Lisicki, beaten in the first round in her four pre-Wimbledon tournaments, landed the first blow with a break in the second game of a rain-delayed opening set.
But 19-year-old Stephens, making her Wimbledon debut this year, had no intention of surrendering without a fight.
Just a month ago Stephens was a lowly 92nd in the rankings, but she has risen to 59th after becoming the first American teenager to reach the French Open fourth round since her close friend Serena Williams in 2001.
She hit back against Lisicki with a break in the fifth game and it needed a tie-break to settle the set.
Stephens looked in pole position as she raced into a 5-2 lead, but suddenly her nerve seemed to fail her and a series of wayward forehands gifted the set to Lisicki.
That could have been a hammer blow to Stephens' morale, but she responded impressively in the second set, breaking twice to restore parity in emphatic fashion.
Lisicki was struggling to cope with Stephens' power and poise and she took a lengthy break before the final set to compose herself.
It worked a treat. She broke midway through the set and eventually coasted into the fourth round.
