The 10th-seeded Dane beat 13th-seeded Errani at her own strategy, engaging in long baseline rallies but using superior power to open the court and find lanes for blasting home winners.
Former world number one Wozniacki belted 15 winners to four for Errani in the first set and, despite losing serve in the opening game of the second set, roared to victory in a brisk 65 minutes at Arthur Ashe Stadium.
Wozniacki's opponent in the semi-finals will be Peng Shuai of China, a 6-2 6-1 winner over 17-year-old Swiss Belinda Bencic.
Peng, 28, delivered a 64-minute master class to 2013 junior world number one Bencic in an unlikely quarter-final between unseeded players.
The Chinese had rattled off three impressive upsets in a row from the second round, ousting fourth seed Agnieszka Radwanska, 28th seed Roberta Vinci and 14th-seeded Lucie Safarova, on her way to reaching her first grand slam singles semi-final in 37 attempts.
"This is amazing time for me," said Peng, who has won 16 doubles titles, including this year's French Open, but is still chasing her first singles crown.
"A lot of tennis. It's a long time, the career. It's tough sometimes. I'm thinking to give up and stop play because I don't know if I can make it or not."
- Sports & Recreation
- Peng Shuai
- Belinda Bencic