Emma Raducanu is the only qualifier ever to win a grand slam title but Yastremska increased her tally of wins in Melbourne to eight with a 6-3 6-4 victory on Rod Laver Arena.
The stories are not exactly comparable, given Yastremska was ranked 21 in the world as a 19-year-old before serving a six-month provisional suspension for a failed doping test, for which she was later deemed to bear no fault.
But it is nevertheless a very impressive run from the Ukrainian, now 23, who is set to soar back into the top 30 from her current ranking of 93.
She is the second qualifier in the open era to reach the last four here in the women's singles after Australian Christine Dorey in 1978.
Yastremska said: "I think it's nice to make history because at that time I still wasn't born. I'm super happy, and tired. I arrived here on January 3. On the days when I have a match, they do go very fast. When I have a day off, it feels like I've been here for six months already."
This was a contest of first-strike tennis, with both women looking to seize the initiative in rallies as early as possible.
But it was the extra power of Yastremska that made the difference, with the Ukrainian hitting 19 winners compared to only six for 19-year-old Noskova.
"I don't really feel like I'm playing really good," said Yastremska, who has beaten Wimbledon champion Marketa Vondrousova and two-time winner Victoria Azarenka during her run.
"I just try to play like I can and take the maximum from myself. Everything I have left is just fighting."
In the last four, Yastremska will take on 12th seed Zheng Qinwen, who will also contest her first slam semi-final.
The 21-year-old, the first player from China to make it this far since Li Na won the title 10 years ago, lost the first set on a tie-break to Russia's Anna Kalinskaya but hit back strongly to win 6-7 (4) 6-3 6-1.
Remarkably, if Zheng goes on to reach the final, she will have done so without facing an opponent ranked in the world's top 50.
She is now guaranteed to be in the top 10 after the tournament, and Zheng said: "She played really good today, especially really good baseline strokes.
"I told myself, 'Stay focused, don't think about the first set'. I'm so happy right now. It's the first time for me. I'm really happy to be in the semi-finals, especially with such a good performance as this."
