Paolini, seeded 12th, is enjoying the best season of her career at the age of 28 after years of toil and a succession of early exits at the biggest tournaments.
"It's an unbelievable feeling," said Paolini, who had never previously made it past the second round at any Grand Slam until this year.
She had two points for a 5-3 lead on her serve in the second set but had to regroup after former Wimbledon champion Rybakina rallied to take the match to a deciding set.
"It was a really tough match. I was a bit too emotional in the second set," added Paolini.
"I said to myself 'ok, it is good'. She (Rybakina) is a great champion so it can happen. I tried to hit every ball and it worked, I am here."
Paolini followed up her singles victory by also making it through to the semi-finals of the women's doubles alongside Sara Errani.
She hopes to go a step further than Errani, who lost the 2012 French Open singles final to Maria Sharapova.
"It's somebody that I think can help me so much. She already did a Grand Slam final, so she already have been in this position," said Paolini.
Contrasting roads
While success was a long time coming for Paolini, who claimed her biggest title - only the second of her career - in Dubai in February, her upcoming opponent is the youngest Grand Slam semi-finalist in 27 years.
Mirra Andreeva has been turning heads since bursting onto the scene in April 2023 when she advanced to the last 16 of the Madrid Open on her WTA main draw debut.
That run, incidentally, was ended by Aryna Sabalenka.
On Wednesday, the 17-year-old Andreeva avenged that defeat with a shock 6-7 (5/7), 6-4, 6-4 over the two-time Australian Open champion.
Andreeva had already ensured she would break into the world's top 30 before toppling Sabalenka, but it wasn't until last season Paolini made that same leap.
"I think I started to play better with more consistency last year," said the Italian, who was a member of the team that reached the 2023 Billie Jean King Cup final, which ended in defeat by Canada.
"I think match by match I felt more convinced that I can play at the higher level but it was a process. (It wasn't) like I switch something," explained Paolini.
"The problem, I think, let's say 'problem,' but it's me that I wasn't believing that I could reach the result that I'm reaching now when I was younger."
That was reflected in her winning a total of four matches in 16 Grand Slam appearances before advancing to the fourth round of the Australian Open in January.
Now she is two wins away in her unlikely quest to emulate compatriot Francesca Schiavone, who won the 2010 French Open.
History suggests whatever Thursday's outcome against Andreeva that time is still on Paolini's side.
Schiavone's Grand Slam breakthrough came two weeks before she turned 30, while Flavia Pennetta - the only other Italian woman to win a major - captured the 2015 US Open aged 33.