The 12th seed raced to a 6-3, 6-2 victory after just 69 minutes on Centre Court and will face Czech ninth seed Linda Noskova for a place in her first major final.
"I was on this court as a spectator once nine years ago watching Roger (Federer) and to be back here as a player is amazing," said the 24-year-old after her first appearance on the showpiece court at the All England Club.
"I walked past the 'wall of honour', stood beside it and took a moment."
Kostyuk has only lost one of her last 22 matches - a semi-final defeat by eventual champion Mirra Andreeva at the French Open last month
Former Wimbledon runner-up Paolini could not reproduce the form she showed in her last-16 win over Alexandra Eala, losing in the last eight of a Slam for the first time.
The in-form Noskova was the highest seed left in the bottom half of the draw after shock early exits for Iga Swiatek and Elena Rybakina.
Two-time Grand Slam champion Coco Gauff or Czech 10th seed Karolina Muchova will await the winner in Saturday's final.