Klaasen, the last South African remaining in the main draw of the Grand Slam tournament, and Butorac fought back from a set down to beat Treat Huey of the Philippines and Dominic Inglot of Great Britain 6-7, 7-6, 6-4 in the quarterfinals.
“The match was epic. We had a great start but then we played a weak game and handed it straight back to them,” Klaasen said.
“It was not going our way and we were almost out of the Australian Open, but we dug deep and fought back, and we’re happy to get the win.”
The 31-year-old Capetonian had achieved his previous best finish in a Grand Slam tournament at the 2012 US Open, when he reached the third round with Alex Bogomolov Jnr.
After romping to surprise wins over Australian duo Lleyton Hewitt and Pat Rafter in the first round, and American top seeds Bob and Mike Bryan in the third, Klaasen and Butorac will face eighth seeds Daniel Nestor of Canada and Nemad Zimonjic of Serbia in the semifinals.
While he has played with Butorac for less than four months, Klaasen believes they have the potential to compete consistently at the highest level.
“We’re feeling very good about our game,” he said.
“We know if we execute properly we can beat any team, and I think we’ve shown that in this tournament.”
Klaasen will return home after the Australian Open to compete in next week’s Davis Cup tie against Monaco in Centurion.
“The Davis Cup is very important to me. It’s my only link to home as a player, so I’m looking forward to it.”