Serving down 0-40, Errani could only watch as Wozniacki hit a forehand crosscourt winner to break serve and take the set 6-0.
In the first game of set two at breakpoint, Errani hit a down the line backhand volley winner to take her only game of the night.
Wozniacki, playing with more baseline aggression than in recent years, broke serve before holding serve and breaking serve again to take a 3-1 lead.
Errani hit three backhand errors as Wozniacki held serve to go ahead 4-1.
With Errani serving, the Dane struck two crosscourt forehand volley winners to lead 15-40.
Wozniacki would then strike a down the line backhand winner to pass Errani at the net and break serve for a 5-1 lead.
With Wozniacki serving for the match, Errani hit a backhand down the line volley winner to reach 0-15 before netting a crosscourt backhand for 15 all.
Wozniacki struck an overhead winner to reach 30-15 before Errani netted a forehand return to fall behind 15-40 and face match point.
The Dane, possessing an overwhelming lead, attempted both first and second serves in excess of 100 miles per hour before double faulting to reach 40-30.
Errani netted a crosscourt forehand to end the quarterfinal after only one hour and five minutes of play.
In the semifinals, Wozniacki will meet the unseeded, 39th ranked Shuai Peng of China.
Should Wozniacki win the semifinal, she could then face her friend, the top ranked Serena Williams of the USA in Saturday’s final round.