The 22nd seed raced past the former French Open champion, seeded 17, in 1hr 19min on Rod Laver Arena and will meet either American Jessica Pegula or Belarusian Victoria Azarenka for a place in the final.
"I'm super happy to be the first time in the semi-finals," said the Kazakh star. "It was an amazing atmosphere."
Rybakina had declared "she could beat anyone" after knocking out top seed Iga Swiatek in straight sets on Sunday.
And she was quickest out of the blocks behind her big serve, breaking Ostapenko immediately and hammering down three aces to reach 3-1.
She created another break point at 30-40 when a sudden cloudburst halted the 22nd seed's momentum.
The players scurried from Rod Laver Arena while the roof was closed and the water mopped up.
After a delay of almost half an hour, Ostapenko saw off the immediate danger.
But she was powerless to prevent the aggressive Rybakina capturing a second break two points later.
Rybakina's serving got her out of trouble in the next at 15-40 and closed out the opening set in 32 minutes
Ostapenko upped the power on her groundstrokes at the start of the second set, breaking for 2-0 with a scream.
But the calm Rybakina broke back and saved four more break points in the next to level at 2-2.
Rybakina struck again in Ostapenko's next service game to put the finish line firmly in sight.
At 6-5 serving for the match, the normally assured Russian-born Kazakh saw two match points saved before her 11th ace sealed her progress.
"Of course I was nervous especially in the last game but not as nervous as before the match," she said. "So I'm super happy that I managed my emotions and I played really well today."
Ostapenko had won both their previous encounters -- the last at Eastbourne in 2021 -- and was also appearing in her first Australian Open quarter-final.
The 25-year-old has been working her way back to the top after admitting she found it hard to cope at 19 when her life was changed by winning the French Open.
After knocking out Coco Gauff in the fourth round, she said her confidence was back and she had "never doubted" she had the ability and drive to win another Slam.
But Rybakina was unstoppable as she chases her second Grand Slam crown in six months after triumphing on the grass at Wimbledon last July.