The German winner, who played the title match here two years ago, beat the 2009 champion on a fifth match point in a see-saw battle on the lawns of Devonshire Park.
The men's semi-final line-up was completed a day late after Spanish third seed Feliciano Lopez, the holder, beat France's Jeremy Chardy 6-3, 6-4 in a quarter-final which was unable to start on Thursday evening due to rain and impending darkness.
Berber broke Wozniacki, a former world number one, on 12 of 17 chances, going up a double break in the final set.
The Pole got one of the breaks back as Kerber was unable to serve out the victory leading 5-2 in the third.
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But the ninth-ranked German ended with a concluding break of her opponent a game later, sending over a cross-court winner to wrap up victory.
She will play in Saturday's final against either Heather Watson or American Madison Keys after improving to 5-3 over Wozniacki in their series.
"I'm so happy to be in the final, I'm feeling very comfortable on grass. I'll go for the title tomorrow just playing my game and trying to be aggressive like I was today."
Kerber will improve her WTA ranking to seventh after reaching her third final of 2014, finishing runner-up in Sydney and Doha in the first two months of the year.