Paolini will face third-seed Elena Rybakina in the semis, after the Russian-born Kazakh took less than an hour to beat Ajla Tomljanovic 6-2, 6-0 later in the day.
Twice Grand Slam finalist Paolini needs a win over Rybakina in the last four to qualify for next month's WTA Finals in Riyadh.
The contest against Bencic at the WTA 500 hard-court tournament, which lasted a marathon three hours and 22 minutes, marked the longest match of Paolini's season.
Bencic, 28, served for the match at 5-4 in the second set but was unable to close it out. Her momentum was further interrupted in the deciding set when she took a medical time-out due to a thigh issue while trailing 4-3.
"One of the toughest I ever played, honestly," Paolini, who was the runner-up at last year's French Open and Wimbledon, said. "Belinda, she's an amazing player and a very good person. Today she deserved to win as well, so it was really tough.
"I'm happy I stayed there, because at the beginning I had too many mistakes. I couldn't find my best tennis, but then I just tried to stay there every point and turn the match somehow."
Aryna Sabalenka, Iga Swiatek, Coco Gauff, Amanda Anisimova, Jessica Pegula and Madison Keys have all qualified for the season-ending championship of the WTA Tour in Riyadh, with two spots still up for grabs.
Rybakina eases past Tomljanovic
Rybakina also remained in contention for a place at the WTA Finals, as she landed seven aces while a struggling Tomljanovic made nine double faults.
Former Wimbledon champion Rybakina has now won 50 matches on the tour this year and qualified for seven semi-finals.
"Of course it would be nice to qualify (for the WTA Finals). But I know for this I still need to win a lot of matches. Not only here, but also next week," Rybakina said.
"Today I think I served well. It’s not easy to play Ajla. Today a lot of things went my way. Also some lines which I caught. Overall, happy I won in straight sets. Looking forward to tomorrow."
Russian fourth seed Ekaterina Alexandrova brushed aside American McCartney Kessler 6-3, 6-3. Alexandrova will next face the winner of the clash between local favourite Zhu Lin and seventh seed Diana Shnaider.
