The Danish 10th seed was in imperious form at a typically windy Arthur Ashe Stadium, dismantling 13th seed Errani 6-1 6-0 in one hour five minutes.
Wozniacki showed an aggressive side to her not often seen, producing 26 winners and only 10 unforced errors.
The former world number one and 2009 US Open finalist got off to a slow start, serving at 0-40 in the opening game.
But if the Italian thought she was in with a chance, she would be quickly mistaken as Wozniacki was dominant thereafter to win the first set in 29 minutes.
Errani broke for a 1-0 lead in the second set, but it would be shortlived - as Wozniacki resembled the form that took her to the top ranking in 2010.
The Italian's downfall was her usual nemesis, her serve, as Wozniacki won all bar eight points on return.
Errani won only five of 28 points behind her first ball, as the Dane powered her way into the semis.
Awaiting Wozniacki is China's Peng Shuai, who celebrated her first appearance in a grand slam quarter-final with a resounding 6-2 6-1 win over Swiss Belinda Bencic.
Peng, 28, has previously been more renowned for her prowess on the doubles court, where she has won two majors, but the world number 39 has made a stunning run at Flushing Meadows.
After knocking out seeds Agnieszka Radwanska, Roberta Vinci and Lucie Safarova, taking care of talented teenager Bencic was Peng's next assignment.
And the Chinese woman did so with ease, progressing in one hour four minutes.
Peng struck 24 winners and a measly seven unforced errors, as Bencic was overwhelmed.