The victory means the No. 2 seed has beaten the unseeded Davenport for the first time in five career meetings, including last week's quarterfinals at the Commonwealth Classic in Bali, Indonesia.
Davenport had an eight-match winning streak snapped.
"This time it was a different story, I tried to play tight and tried to move her around," Jankovic said.
"I couldn't move as quickly as I wanted," said Davenport, who recently gave birth to her first child. "It was too much tennis for me. Today my legs felt heavy, but I exceeded my expectations."
Late in the second set, Jankovic slammed a ball that hit Davenport.
"I was really frustrated, but it was an accident," Jankovic said.
In Sunday’s final, Jankovic will face 18-year-old Hungarian Agnes Szavay, an easy 6-1, 6-2 winner against China's Peng Shuai.
The winner will claim $88,265.
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