The Dane, a former world number one, will play Germany's Angelique Kerber on Sunday as she eyes her second title of the year. Kerber eased past American Madison Brengle in straight sets, 6-3 6-1
Wozniacki clinched the first set after more than an hour when Halep sent a backhand into the net.
The world number three, who had 22 unforced errors in the first set, upped her game, racing to a 3-0 lead before being reined in by Wozniacki's thundering groundstrokes.
Halep, who has won three titles this year, levelled but quickly fell two breaks behind again in the third as Wozniacki went 5-1 up.
Halep saved three match points but could do nothing in the next game as Wozniacki clinched victory after two hours and 58 minutes.
Kerber, who eliminated title holder and top seed Maria Sharapova as well as sixth seed Ekaterina Makarova in the two previous rounds, had little trouble against the world number 43.
Too many unforced errors proved costly for Brengle, whose flowing baseline play troubled the German only in the first set as Kerber claimed a stake at becoming the first German since Julia Goerges in 2011 to win the tournament.
The world number 14, who needed 58 minutes to seal her victory, is on track for a second title of the year after winning in Charleston, South Carolina earlier this month following a bad start to the year.
(Reporting by Karolos Grohmann, editing by Ed Osmond/Gene Cherry)
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