The confident cueman from Melbourne clinched a brilliant 13-8 victory over world number two Stephen Maguire, and will take on Shaun Murphy next.
Robertson and Maguire slugged out a slow-paced afternoon session which included a frame lasting one hour and three minutes.
But the gutsy 27-year-old from Down Under dominated the early play this evening before fending off the threat of a fightback from Maguire to seal his semi-final place.
The late Eddie Charlton was the last Australian to reach the last four in Sheffield, 27 years ago. He was knocked out by Ray Reardon.
Robertson takes his place in a youthful-looking semi-final line-up, which also features 23-year-old Northern Irishman Mark Allen and 26-year-old Murphy.
“Tonight was great. My long game was absolutely fantastic and I think it must have killed him,” Robertson said.
“I dropped in three long reds in consecutive frames and cleared up every time. That was a big blow to him. This is a great moment.”
Beaten Maguire was disgusted with his performance. “It was pure rubbish, embarrassing at times,” he said. “I kind of knew what the result was going to be early on today and all I was doing was delaying it.
“I’m so disappointed in myself that I never even stood up to a little challenge. I gave him an easy pass through to the semis and I’m raging with myself.”
Earlier Stephen Hendry bowed out and admitted a seventh-frame 147 break sparked his collapse. The seven-time champion took a 5-2 lead over Murphy after producing his magical maximum, which will earn him £157,000 unless anyone matches it over the final five days.
But the Scot could not maintain the intensity of his early performance, and Murphy sealed a 13-11 victory.
“After I made the maximum my concentration was nowhere,” Hendry said. “If I’d missed on around 70 or 80 and gone 5-2 up I’d still have had that same intensity in my concentration to win the next frame. But with the maximum I was so elated. It’s probably the biggest buzz you can get in snooker.
“In the next break I missed a red Willie Thorne would pot.”
Murphy was elated with victory against the player who crushed him in his first Crucible match in 2002.
“I made my debut against Stephen as a 19-year-old and he beat me 10-4, completely beat me up, embarrassed me in front of my friends,” Murphy recalled.
“And to beat him here, a guy who’s back to his best and playing really well, I put that down as one of the biggest victories of my life.”
Allen joined Murphy in the semi- finals after a 13-11 victory over Welshman Ryan Day, and was delighted to prove his second-round win over Ronnie O’Sullivan was not a fluke.
He said: “A lot of people were quick to shoot me down after beating Ronnie, as being a one-hit wonder. So there was more pressure on me but I enjoy that, because I like to prove people wrong.”
Meanwhile, John Higgins clinched a dramatic deciding-frame victory over Mark Selby to secure a place in the semi-finals.
Higgins had looked set for a last- eight exit but turned around his match against Selby to win 13-12 and set up a clash against Northern Ireland’s Mark Allen.