An escape act from Cocciaretto gave the defending champions the opening point of the tie, the Italian digging deep to post a 4-6, 7-5, 7-5 win over Yue Yuan.
Paolini sealed the victory by defeating Wang Xinyu, who squandered a one-set lead and early breaks in the second and third sets to fall 4-6, 7-6(4), 6-4 to the world number eight.
"It was a really tough one. Xinyu was playing really good tennis," said Paolini, who secured Italy’s place in the semi-finals for a third straight year.
"Today was a bit tough for me, but I tried to stay there for everyone that was on the bench, the Italian fans, for the country."
Earlier at the Shenzhen Bay Sports Centre Arena, in a two-hour 52-minute battle, Cocciaretto wiped a 2-5 deficit in the second set, and a 0-4 deficit in the decider before securing the victory.
Yue was cruising at 6-4, 5-2 before her Italian opponent launched a comeback, taking the next five games to level the match.
"For sure, it was a tough moment. She was playing unbelievable, and I wasn't too aggressive," said Cocciaretto of her mindset at 2-5.
"Something changed in my mind and I said, ‘Go for it, be aggressive, and no matter what, don't think about the score, just try your best and fight'. And that's what I did."
Yue responded by winning the first 14 consecutive points of the third set en route to a 4-0 advantage. But once again, Cocciaretto fought back, clawing her way to 5-5 and claiming a decisive break in the 11th game to deliver a blow to the home fans.
"It was the first match of the Billie Jean King Cup, facing the home team. I knew that there was tension between us," said the 92nd-ranked Cocciaretto.
Tennis legend Billie Jean King attended the match, and Cocciaretto admitted she was nervous at the start when she spotted her in the stands.
"I said to myself, 'Don’t think and don’t watch her, please, because if not, you don’t think about the game'.
"But I'm really honoured to play this match and see her in the crowd," added the 24-year-old.
In the semi-finals, Italy will face the winner of Wednesday's clash between Spain and Ukraine.
