Italian third seed Paolini broke twice as she dominated the first set but the second set was more even as the players swapped breaks.
However, Paolini, who lost to Iga Swiatek at Roland Garros earlier this month, stepped up a gear in the tie-break, winning seven straight points to seal victory.
"Today I played a really good match," Paolini, 28, said in her on-court interview.
"She's a really good player on grass, of course she's British, so it's tough to beat her here, especially. I'm happy, I'm enjoying the grass here in Eastbourne."
Boulter, ranked 32nd in the world, came to Eastbourne in good form after retaining her Nottingham Open crown earlier this month.
Russia's Kasatkina eased through 6-2, 6-2 against Britain's former US Open champion Emma Raducanu, who celebrated her first win over a top-10 player on Wednesday, ousting second seed Jessica Pegula.
The sixth seed broke Raducanu twice in the first set to take a grip on the match.
Both players struggled on serve in the second set, with a total of six breaks, but the Russian held to complete the win when Raducanu went long with a forehand.
Canadian world number 30 Leylah Fernandez advanced to her first semi-final of the season, defeating Britain's Harriet Dart 6-2, 6-1.
Fernandez will face defending champion Madison Keys in the last four after 2023 French Open finalist Karolina Muchova withdrew due to a right wrist injury.
"I'm sad to withdraw from today's match," Muchova said in a statement. "I'm sorry to fans but I have to follow my medical team's advice and rest up for Wimbledon."
In the men's competition, Britain's Billy Harris continued his fairytale grass-court season, beating Flavio Cobolli 6-7(3), 7-6(4), 6-2.
Harris, who reached his first quarter-final last week at Queen's, until recently travelled to tournaments, and slept, in a converted van.
Australian qualifier Max Purcell beat Serbia's Miomir Kecmanovic in straight sets while Aleksandar Vukic, another Australian, came out on top in a third-set tie-break against Yoshihito Nishioka.
Two-time champion and top seed Taylor Fritz is in action later.
