World number five Del Potro was dragged into a scrap by Radek Stepanek and needed to recover from a mid-match meltdown before fending off the Czech veteran 6-4 3-6 6-3 to set up a clash with 2008 champion Dmitry Tursunov.
Mixing patchy phases with occasional flashes of brilliance, the 2009 U.S. Open champion appeared close to losing his cool at times and joked that only his shortage of racquets had prevented him from slamming one into the hardcourt in frustration.
Del Potro has stuck to his older-generation Wilson racquets religiously but has only two left, and is reluctant to change to a new one before the year's first grand slam.
Fiery Cypriot Marcos Baghdatis famously destroyed four of his racquets during a loss against Swiss Stanislas Wawrinka at the 2012 Australian Open, and Del Potro said he had been similarly tempted when struggling against Stepanek.
"Yeah, I was close, but I can't do that yet. When I get eight or ten racquets, I will smash all of them," he quipped to reporters.
Defending champion Bernard Tomic strolled past Alexandr Dolgopolov 6-4 6-3 and will meet another Ukrainian in Sergiy Stakhovsky in the other semi-final.
Despite crashing out of the semi-finals to 107th ranked Tsvetana Pironkova, second seed and former Wimbledon champion Kvitova was relaxed about her 6-4 6-3 loss three days ahead of the start at Melbourne Park.
"I think the matches I played were great, and I have three under my belt," the Czech world number six said.
"So I think it's really good to have this record coming to Australian Open."
Pironkova, a one-time Wimbledon semi-finalist, is the first qualifier to reach the Sydney final and will battle German Angelique Kerber, who swatted aside Madison Keys in straight sets, for the title.
In Melbourne, world number seven Tomas Berdych advanced to Saturday's final in the invitational Kooyong Classic with a 6-4 6-1 victory over Japan's top-ranked Kei Nishikori. Berdych will play the winner of an all-French semi-final on Friday between Richard Gasquet and Gilles Simon.
Thirteen proved an unlucky seeding in Melbourne for a second year in a row as Spaniard Nicolas Almagro was forced to pull out of the year's first grand slam with a shoulder injury.
Last year's 13th seed John Isner also withdrew three days before the tournament due to a troublesome knee.
(Reporting by Ian Ransom; Editing by Justin Palmer)
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