The world number 15 had top seed Sharapova on the back foot early in the first set, forcing her into a string of uncharacteristic errors, and did not let up until she had gained revenge for her semi-final defeat by the Russian last year.
Lisicki, who had complained about her second-round opponent Bojana Jovanovski's grunting, was forced to endure Sharapova's loud wails, but kept her concentration to break the French Open champion decisively in the 10th game of the first set.
She broke again early in the second and closed it out, converting her third match point with an ace, to set up a quarter-final against compatriot Angelique Kerber who crushed Belgium's Kim Clijsters 6-1 6-1 in her final Wimbledon.
"It is just unbelievable for me, I'm just so happy," Lisicki said after falling to her knees with both fists clenched in celebration.
"I have lost my three previous meetings with her. I just went for my shots...
"I am a fighter too and I fight to last point. I'm getting better with each match."
Clijsters, one of the most popular players on the circuit, who is retiring for a second time after the US Open, was certainly not wallowing in nostalgia and self-pity.
"Not at all," she told a news conference. "I just had the feeling that there was absolutely nothing I could have done today to win the match."
The memories flooded back as she recalled how her father always sat in the same seat every day because he thought it would bring her luck, but the English weather spoiled the fairy story.
"He was here for three or four days and I don't think he saw me play for one minute because it rained for three days in a row," she said.
Clijsters, who never reached the Wimbledon final, retired from tennis in 2007 to have a family and her father died before she made a spectacular comeback in 2009 and won the US Open weeks later.
The other quarter-final in the top half of the draw will see Agnieszka Radwanska face Mario Kirilenko.
Third seeded Pole Radwanska booked her place in the last eight thanks to a 6-2 6-3 win over Camila Giorgi.
Russian 19th seed Kirilenko reached just her second Grand Slam quarter-final with a 6-1 6-7 6-3 triumph over China's Shuai Peng.
Defending champion Petra Kvitova came back from a set and a break down to beat Italian Francesca Schiavone 4-6 7-5 6-1 in a rain-disrupted match.
Kvitova, the fourth seed, looked to be in trouble when former French Open champion Schiavone went a set and 2-1 up, taking advantage of a double fault to help her break the Czech.
Kvitova, however, broke straight back and went 6-5 up before light rain began falling on Court Three.
The match continued after a series of stops and starts, with the players sitting on their chairs, wrapped in towels and sheltering under umbrellas, while officials waited to see if the rain would stop.
Schiavone was clearly unhappy at being told to resume play early in the third set, complaining to no avail that the grass was damp and slippery.
As Kvitova stood waiting to play, British umpire Fiona Edwards urged Schiavone back on to the court, saying: "Can we at least try? I will watch you."
The Italian relented but she continued to glower and mutter as Kvitova raced through two breaks of serve to wrap up the set in 39 minutes, finishing off with a love game.
Schiavone said she had been unhappy at the indecisiveness of the umpire.
"When it is damp you should say yes or no, not just stay there and wait," she told a news conference. "But that is not an excuse (for losing), of course.
"I am sorry because I knew how I was playing," she added. "I knew how much this match counted. I was playing a good game, I was winning."
Kvitova sympathised with Schiavone but said she had been keen to play on despite the weather.
"The grass was a little bit damp so it was a little bit dangerous but I was ready to play on, to continue, because I knew that I had a chance," she said.
"When I made the break finally, after one hour or however long we had played, it was better for me."
Kvitova, who had not dropped a set in the first three rounds, will now face former champion Serena Williams.
Four-times champion Williams withstood a stiff test from Yaroslava Shvedova to reach the quarter-finals with a 6-1 2-6 7-5 win.
Kazakhstan's Shvedova, who became the first player to win a set at a Grand Slam without dropping a point in the previous round, troubled the American as the dark clouds gathered above Court Two but was undone by a late flurry of pace and power.
Williams, the sixth seed, took just 26 minutes to race to a first set lead. She dominated with her more powerful serve and ground strokes but was made to work much harder from then on as Shvedova found her rhythm.
The American, watched by her sister Venus and her father, went down a break at 4-2 in the second as she started to struggle with her movement.
Shvedova began hitting the lines with a piercing backhand that had Williams flailing and she sealed the set with another screaming effort that sailed past the American.
With Williams's performance so far as temperamental as the British Wimbledon weather, the final set was a much more even contest, both women exchanging blows in lengthening rallies.
Four break points came and went for Williams as Shvedova dug in with some brilliant shots. But the Kazakh was undone by two double faults that put her in trouble and left her 6-5 down.
With light rain now trickling down on court Williams produced a superb lobbed backhand in the final game that had the crowd cheering before a blazing backhand sent Shvedova lunging in vain and sealed victory in just under two hours.
"I felt fine out there I think we both wanted to keep playing because it was so deep into the match," Williams said.
"I'm not tired so I feel good. I feel like I can play so much better than what I have been playing."
The 21st seed Roberta Vinci was beaten 6-2 6-2 by unseeded Austrian Tamira Paszek, who won the warm-up tournament at Eastbourne, and Victoria Azarenka awaits after destroying Ana Ivanovic 6-1 6-0 on Centre Court in 62 minutes.
Belarussian Azarenka completely outclassed the former French Open champion, seeded 14th, moving her relentlessly around the court with a succession of accurate and powerful groundstrokes.
Azarenka's main problem in the second set was a pigeon trapped under the Centre Court roof but she calmly removed a few feathers which fluttered on to the playing surface before resuming her impressive performance that included only six unforced errors.
The Australian Open champion sealed victory when Serb Ivanovic netted a backhand.