Earlier, Elisabetta Cocciaretto produced a gritty comeback to edge out Yuan Yue 4-6 7-5 7-5, rallying from a set and 2-5 down and 0-4 behind in the deciding set, to give Italy the opening point. Both matches lasted nearly three hours.
"It was a tough match and tough conditions because we are playing against the host country," said Cocciaretto, ranked 91st in the world.
"I said to myself to turn up the match and just think about the game and just the strategy and not about the results and the score. I tried to do it and I think it works."
Paolini had looked on the brink of defeat when trailing 3-5 in the second set on Tuesday, but the Italian broke back and dominated the tiebreak to level.
She then withstood a third-set surge from Shenzhen-born Wang, ranked 34th in the world, reeling off four games in a row to avoid a deciding doubles contest.
"It was a really tough day. Two matches, both really tough. Both of them we almost lost the match and somehow we turned it around," said Paolini.
"I think I was a bit nervous, I couldn't focus on my game 100 per cent and that's why I think my level was a little bit going up and down.
"Hopefully for the next round I'm going to be more positive, more relaxed and enjoy more the match because we have to raise the level a little bit in the semi-final."
Italy next play the winners of Wednesday's quarter-final between five-times champions Spain and Ukraine.
Kazakhstan, who knocked out Australia in the qualifiers, United States, Great Britain and Japan are the other finalists.Â
