The 34-year-old, whose only other appearance in the last four of a grand slam was against Steffi Graf at Wimbledon in 1999, will play world number two Serena Williams in the semi-finals after the American beat Britain's Johanna Konta.
The German-born righthander won her first singles match at Melbourne Park in 1998 but had to wait 19 years for her second victory in the year's opening grand slam last week.
Reaching the last four was beyond her wildest expectations.
"I can't believe this, this is crazy," she said. "I can't believe I'm in semi-finals again. I feel a little bit in shock right now."
The incredible run almost came to an end on Wednesday when the pain got too much to bear for Lucic-Baroni, who played with heavy strapping around her left thigh and calf.
Trailing 4-3 in the deciding set, she took a five minute medical timeout and was still limping when she returned. But somehow she lifted her game to a new level, rattling off 12 of the next 13 points to race through the final three games and close out the match.
"I was really worried. I didn't know if I had it in me to finish it," Lucic-Baroni told reporters. "I started hurting pretty bad mid-match, especially at the end.
"I was really concerned with my physical well-being at that point. And I just said to myself, 'They're either going to wheel you out. I'm not going to give up, just keep fighting'.
"And that was it."
The timeout changed the momentum of a match that had already produced several twists and turns, with both players seizing the advantage at certain points but never really dominating.
