Boulter beat reigning Australian Open champion Rybakina 7-5, 2-6, 6-4 to seal her second victory in the space of a few hours on the grass at the Wimbledon warm-up event.
Boulter had defeated Romania's Jaqueline Cristian 6-1, 6-3 earlier in the day before returning to stun top seed Rybakina in the evening.
The 29-year-old, ranked 73rd in the world, showed no signs of fatigue as she wore down Rybakina, who won Wimbledon in 2022, in a gruelling clash lasting over two and a half hours.
In Saturday's semi-final, Boulter, who was given a wildcard entry into the tournament, will face Croatia's Donna Vekic, a 6-4, 4-6, 6-3 winner over Karolina Pliskova in the last eight.
Rybakina was also playing for the second time in the day after ending Tatjana Maria's reign as Queen's champion with a 6-7(4), 7-5, 6-0 win over the German.
Former US Open champion Emma Raducanu clinched a place in the quarter-finals for a second successive year with a 6-4, 6-2 win over Romanian seventh seed Sorana Cirstea.
It was a cathartic victory for the British number one, who lost to Cirstea in the Cluj-Napoca final in February.
"Earlier in the year she beat me, but I'm glad I could get her back at home as well," Raducanu said after her first win against a top-20-ranked opponent in over a year.
"I think I played a really high level. I knew I had to."
Raducanu will play her delayed quarter-final on Saturday against Uzbekistan's Kamilla Rakhimova, who beat British wildcard Harriet Dart.
The winner of Raducanu's meeting with Rakhimova will play American sixth seed Iva Jovic in the semi-finals.
Jovic beat former Wimbledon runner-up Amanda Anisimova 6-2, 3-6, 6-3.
