Lisicki, a 15th-ranked German, outplayed the 2004 Wimbledon champion in windy, rainy conditions on Court 1 for her first career victory over Sharapova in four matches. She avenged a loss in the semifinals to Sharapova here last year.
Also advancing were four-time women's winner Serena Williams, defending champion Petra Kvitova and second-seeded Victoria Azarenka, but four-time Grand Slam champion Kim Clijsters lost in what she says is her final Wimbledon before retirement later this year.
In men's play, six-time champion Roger Federer was the first to reach the quarters, overcoming an early back problem to beat Xavier Malisse 7-6 (1), 6-1, 4-6, 6-3 and extend his record for most consecutive Grand Slam final-eight appearances to 33.
Federer said his back started hurting in the first few games of the match but he felt much better after taking a medical timeout and receiving treatment.
"I feel way better than a few hours ago," Federer said after the match. "Honestly, I'm not too worried. I've had bad backs over the years. I just have to keep an eye on it now ... I hope I'll be 100 per cent on Wednesday."
Sharapova, who won the French Open four weeks ago for her fourth Grand Slam title, is the biggest name knocked out of the tournament since two-time men's champion Rafael Nadal was upset last week by Lukas Rosol.
After smacking a second-serve 108 mph (174 kph) ace down the middle on her third match point, Lisicki collapsed to her knees on the grass and shook both fists. Among those cheering for Lisicki in the guest box was German NBA star Dirk Nowitzki of the Dallas Mavericks.
"It's just unbelievable," Lisicki said. "For the third time I've beaten the French Open champion here. I'm just so happy. I've lost the three previous meetings against her. Now I just played well and beat her for the first time."
Sharapova was trying to become the first woman since Serena Williams in 2002 to win the French Open and Wimbledon in the same year.
"I just went for my shots. Really from the first point on I felt great out there," Lisicki said. "It's my favourite tournament, I love playing on grass, I love the crowd here. I just love it."
Lisicki will next face fellow German and No. 8 Angelique Kerber, who drubbed Clijsters 6-1, 6-1. The 47th-ranked Belgian has said she is retiring after this year's U.S. Open — this time for good, having returned to the sport in 2009 after a two-year break. Clijsters, who has been dogged by injuries this year, walked off Court 3 with a brief wave. Third-seeded Agnieszka Radwanska also advanced, beating Italian qualifier Camila Giorgi 6-2, 6-3.
Azarenka, the Australian Open champion, routed 14th-seeded Ana Ivanovic 6-1, 6-0 in match that was played under the Centre Court roof from 4-1 because of rain. The match was briefly held up at 4-0 in the second set when Azarenka helped the ball boys pick up pigeon feathers that floated down onto the court from the roof.
Azarenka, Williams and Kvitova are the only women's players left who have reached a Grand Slam final — and they're all in the bottom half of the draw. Sharapova's defeat means there will be a first-time finalist from the top half.
Leading Malisse 4-3 in the opening set, Federer called for a medical timeout and left Centre Court with the trainer for treatment in the locker room. When play resumed eight minutes later, Federer didn't seem visibly affected — although the speed on his first serve lacked its usual velocity.
Still, in the final game, Federer hit two serve winners and closed out the match with a 122 mph (197 kph) ace. He'll next play Mikhail Youzhny, who beat Denis Istomin of Uzbekistan in five sets.
"I felt the back going at the beginning of the first set," Federer said. "It must be a mix of maybe the five-setter (against Julien Benneteau in the third round), two days off, the cold wind today. I was unlucky in this regard. Fortunately, I pulled out the match today."
The sixth-seeded Williams won the last three games of the final set to beat 65th-ranked wild card Yaroslava Shvedova of Kazakhstan 6-1, 2-6, 7-5, in cool and gusty conditions on Court 2.
Williams hopped in joy with both feet in the air after hitting a big forehand that forced an error by Shvedova on the first match point, ending a hard-hitting contest that lasted nearly two hours.
"I didn't want to lose today and I thought, 'Just stay relaxed,'" Williams said. "I knew the whole match I could play better."
Williams will next face Kvitova, who rallied from a set and a break down to beat former French Open champion Francesca Schiavone 4-6, 7-5, 6-1 in an error-strewed match on Court 3.
It was the second straight tough three-setter for Williams, who won 9-7 in the third to beat Zheng Jie in the third round.
"I feel fine," she said. "I'm not tired. I'm not anything. I feel good. I feel like bottom line I can play so much better than what I have been playing ... You know me. I'm never satisfied."
The match ended in a slight drizzle, with play suspended on some of the other courts. Shvedova removed her glasses in the final two games to keep the lenses from getting wet.
"I think we both wanted to keep playing because it was so deep into the match," Williams said. "I didn't want to stop.
Williams finished with 35 winners, including 12 aces, and 13 errors. Shvedova had 24 winners and 20 errors.
The first player to reach the quarters was 37th-ranked Austrian Tamira Paszek, who beat Italy's Roberta Vinci 6-2, 6-2 to reach the final eight for the second year in a row.