As expected between two of the biggest hitters on the women's tour, this was first-strike tennis, but Rybakina was the steadier in a 6-2 6-4 victory on Rod Laver Arena.
Both had caused upsets in the previous round, Rybakina defeating world number one Iga Swiatek and Ostapenko powering past Coco Gauff.
The Latvian, French Open champion in 2017, was through to her first grand slam quarter-final for nearly five years, but produced too many errors to put any real pressure on Rybakina.
The Kazakh number one, who is edging closer to the top-10 position she would have occupied had Wimbledon offered ranking points, broke serve to open the match and was 3-1 ahead when a heavy shower caused a delay and led to the roof being shut.
Rybakina maintained her momentum on the resumption to take the first set and, although Ostapenko, who again continually complained about the accuracy of the automated line calling, opened up a 2-0 lead in the second, she could not hold onto it.
Almost three-quarters of the points were decided within four shots while Rybakina's serve, the best in the women's game following Serena Williams' retirement, yielded 11 aces and was a key difference between them.
The 23-year-old will take on either Jessica Pegula or Victoria Azarenka in her second grand slam semi-final.
"I'm super happy to be in the semifinals for the first time," said Rybakina. "Of course, I was nervous, particularly in the last game, but I'm happy I managed my emotions. I played really well today."
Rybakina will play the winner of Tuesday evening's quarterfinal between third seed Jessica Pegula and former two-time Melbourne Park champion Victoria Azarenka.
"For sure, I'm going to watch it," she said. "But at the same time, I need to forget about tennis just for a few hours, to rest the mind, then prepare for another tough match."