Kerber, ranked 14th in the world, completed a memorable week where she beat top seed Maria Sharapova and sixth seed Ekaterina Makarova in previous rounds.
"I am completely done here, empty. I gave everything I had and the crowd just carried me," she said in a courtside interview. "I had to fight until the very end and I could not have done it without this crowd."
Dane Wozniacki, a former world number one, eased past the German in the first set before her game unravelled in the second.
Wozniacki composed herself and a break at 4-3 in the third seed looked to have given her the edge in the indoor arena.
But Kerber, clutching her bandaged right thigh, battled back to win three games in a row to go 6-5 up.
Wozniacki saved three match points before the 27-year-old Kerber kept her cool to convert her fourth chance for her second title in a month after Charleston.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
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