The German 23rd seed, who also made the last-four as a wildcard in 2011, goes on to face either Polish fourth seed Agnieszka Radwanska, the runner-up to five-time champion Williams last year, or Chinese sixth seed Li Na for a place in the final.
"It was an amazing match yesterday, but I had to make sure that I had calmed down and was ready for today," said Lisicki, who completed victory in her fourth Wimbledon quarterfinal just before rain began to fall.
"I have had experience of other years to help me. I also played the semifinals in 2011 so that helped me be ready for today."
Lisicki, who was defeated by Maria Sharapova in the semifinals two years ago, insisted that she felt no pressure coming into Wednesday's match having downed Williams in the fourth round.
"There's no pressure. I just keep playing the game that I love," she added.
Lisicki showed no signs of a hangover from her two-hour, three-set triumph over Williams 24 hours earlier as the 23-year-old Florida-based German broke the world number 46 Kanepi in the opening game on a half-full Court One.
She backed it up with another solid break in the ninth game to take the opening set.
Lisicki, whose ranking slumped to 218 in March 2011 as she battled a career-threatening ankle injury, suffered a brief wobble when she was broken for the first time in the third game of the second set by the 2010 quarterfinalist.
But she levelled immediately before going on to claim five of the next six games to clinch victory inside just 65 minutes on the back of 23 solid winners.
Later Tuesday, 2011 champion Petra Kvitova, the highest seed left in the bottom half of the draw following the shock first week exits of Sharapova and Victoria Azarenka, takes on Belgium's Kirsten Flipkens.
Czech eighth seed Kvitova, the only player born in the 1990s to win a major, is bidding for a third Wimbledon semifinal.
Flipkens, the 27-year-old 20th seed, is playing in her first Grand Slam quarterfinal.
She missed the tournament last year after spending two months away from the sport battling blood clots in her legs, an absence which saw her ranking plummet to 262 in the world.
The winner of that tie will face either French 15th seed Marion Bartoli, the 2007 runner-up, or American 17th seed Sloane Stephens, who was a semifinalist at the Australian Open this year. – Sapa-AFP