The tie was locked at 1-1 on Saturday after French Open and Wimbledon runner-up Paolini beat 56th-ranked Moyuka Uchijima 6-3 6-4 in the second singles match to put the Italians on the board.
While the opening set of that match was all one-way traffic, the second was level at 4-4 before world No.4 Paolini pulled away with the win in little over one hour.
Paolini then returned for the doubles with Errani, who has five grand slam titles to her name. The pair, who won gold together at the Paris Olympics, dominated to beat the Japanese duo 6-3 6-4.
After Japan were 5-1 down in the second set, Aoyama and Hozumi showed great spirit to make it 5-4 but their resistance was short-lived as the Italians sealed the win.
"The strategy was to serve well and try to be aggressive because the game was really fast. They played amazing in doubles, so it was a really stressful match. But in the end, I'm grateful that we did it as a team," Paolini said.
"This year I'm a little bit used to it," the 28-year-old smiled, when asked about playing singles and doubles back-to-back.
"But I will rest now, I will work with the physios here. I have to thank them, working with us and behind the scenes."
Earlier, American-born Japanese Ena Shibahara, ranked 135th in the world, battled back from a set down to beat 54th-ranked Elisabetta Cocciaretto 3-6 6-4 6-4.
Four-times Billie Jean King Cup champions Italy, who were runners-up to Canada in 2023, last won the title in 2013.
They will face either Poland or the Czech Republic for a place in the final.
