Jake White's men scraped home in nerve-wracking circumstances at the Canberra University Stadium after Riaan Smit missed a late kick that would have taken the qualifying fixture into 20 minutes of extra time.
Four penalties from Christian Lealiifano - the man who kicked the Qantas Wallabies to their second Test victory over the Lions in Melbourne three weeks ago - and another from scrum-half Nic White, proved enough for the hosts even though the Cheetahs crossed for a brace of tries.
Johann Sadie's early score and Ryno Benjamin's touchdown at the death ensured things were far less straightforward than the Australian Conference Champions would have liked but it is they who march on to a last-four meeting with the Bulls in Pretoria.
The win means captain Ben Mowen and co still have a chance of claiming a first Super Rugby crown since 2004, just two seasons after they finished a lowly 13th with only four wins from 18 fixtures.
"You always worry when a South African guy's having a kick because they are usually dead on the money," said Mowen, who started all three Tests for the Wallabies against the Lions but wasn't at his best at the weekend.
"It was a big relief. I asked (assistant coach Stephen Larkham) before the kick what was the next part of the game and he said another 20 minutes extra time. I was thinking: 'another 20 minutes of this pace, it could bust right open'. Both sides were out on their feet.
"Fortunately for us it didn't happen…it fell our way. It's good to grab a win here but we're going to build now and try to run all the way through."
The Reds no longer have the chance to 'run all the way through' to an all-Australian final, though, after they were put to the sword by the Crusadrers in Christchurch.
The Queenslanders failed to give Ewen McKenzie the send off he would have liked after they were thrashed 38-9 by the most successful side in the history of Super Rugby despite the fact that they welcomed back Wallaby duo Will Genia and James Horwill for the first qualifying fixture.
McKenzie's men shipped four tries in a disappointing display in New Zealand that saw the Reds' hopes of a second Super XV title in three seasons emphatically ended by Dan Carter and co. Both Horwill and Genia admitted that it was a hugely frustrating way for McKenzie to finish his four-year reign before replacing Robbie Deans in the national hotseat.
"He's a massive part of what this team has been about for the last four years and he deserved better than a performance like that to be sent out on," said Horwill, whose Reds squad will also be without Digby Ioane (Stade Francais), Radike Samo (Japan), Jono Lance (Waratahs) and Luke Morahan (Force) in 2014.
"We spoke before the game about sending out those guys on a good note," added Genia.
"We didn't play well and that's even more disappointing, the fact now they leave on a poor performance. We were just outclassed."
Super XV semi-finals
Chiefs v Crusaders, Hamilton, Saturday, 7.35am BST
Bulls v Brumbies, Pretoria, Saturday, 4.05pm BST