Lisicki, the first German woman to make that far since seven-times winner Graf in 1999, saw off French ninth seed Marion Bartoli on Tuesday to set up a clash with Russia's 2004 champion Maria Sharapova on Thursday.
"Have we finally got another Steffi?" asked the daily Bild newspaper, carrying a photo of the 21-year-old big-hitter from Berlin on its front page, while the Süddeutsche Zeitung said she was "following in Graf's footsteps."
"Sabine Lisicki is showing the world that things are happening in the homeland of Steffi Graf," the Frankfurter Rundschau said - even before her quarterfinal victory.
The British press have also taken to Lisicki, who has quickly been nicknamed 'Doris Becker', 'Boom Boombine' (both referring to retired German tennis star Boris Becker) and simply 'Super Sab'.
Lisicki recovered from wasting three match points in the second set to defeat Bartoli, the 2007 runner-up, who had defeated four-times winner Serena Williams in the fourth round.
"I played unbelievable tennis. I was the better player. I knew I just had to keep fighting in the third set and that I could do it," Lisicki said.
Lisicki had already been a quarter-finalist in 2009 before disaster struck in 2010 when an ankle injury picked up in Miami sidelined her for five months and sent her ranking plummeting to 218.
Graf and fellow German Boris Becker were towering figures in world tennis in the 1980s and 1990s, with Graf, now married to US legend Andre Agassi, winning 22 Grand Slam singles titles.
Lisicki told Bild she has already been for dinner with Graf and Agassi in Las Vegas.
"They are both amazing people. It was great to see how they have stayed down-to-earth despite all their huge successes. It was an honour to meet them."
"Steffi was the last one in the semi-finals," the Tagesspiegel quoted her as saying. "Now it's me. That's unbelievable."