In a stunning first-set collapse, Paolini was 4-0 up but lost the next five games before Shnaider then forced a tiebreak, which the 21-year-old Russian dominated.
Backed into a corner, world No.5 Paolini mounted a comeback of her own in the second set, winning six successive games after herself trailing 4-0.
Down a break in the decider, French Open runner-up Paolini continued to show resilience with the crowd behind her to became the first Italian woman to reach the last four of the WTA 1000 event since doubles partner Sara Errani just over a decade ago.
"It was a good thing that it rained for five minutes. I got some coaching from Sara," Paolini said of Errani, who was watching from the stands.
When Paolini took control in Tuesday's third set, the crowd began singing, "Ole, Ole, Ole; Jas-mine, Jas-mine."
The last Italian woman to win the Italian Open was Raffaella Reggi, who took the title in 1985 in Taranto.
Paolini's semi-final opponent will be either two-time Rome champion Elina Svitolina, the 16th-seed, or unseeded American Peyton Stearns, whose match was delayed by a lengthy break for rain.
The other half of the draw has gone with seeding and on Wednesday Coco Gauff (seeded 4) faces Mirra Andreeva (7) and Aryna Sabalenka (1) plays Qinwen Zheng (8).
with AP
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