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.
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.
In Auckland, David Ferrer and John Isner scraped into the semi-finals after they both struggled through three-set matches.
Ferrer claimed his 14th successive win at the Heineken Open as he ousted compatriot Guillermo Garcia-Lopez 6-3 5-7 6-4. The No. 1 seed's serve deserted him throughout large parts of the contest and subsequently faced 10 break points - though he saved seven of them.
"It was a very tough match with a lot of rallies and long points," said Ferrer. "But I feel good. I played better than last night and I'm happy because I'm in the semi-finals. I played more aggressive, nothing seems like yesterday."
Isner came through a close match with Philipp Kolschreiber 6-7(4) 7-6(4) 7-6(5). The contest lasted two hours and 24 minutes and didn't have a single break of serve.
"Every time I've played him it's been very close," said Isner. "I tend to play a lot of close matches regardless, but especially against him. It was super close and very competitive. There's some things I definitely could have done better. But all in all I'm happy. I served unbelievably well today and that's the only reason I won."