The semifinals were postponed on Friday because of rain. Organizers planned to play both the semifinals and finals on Saturday.
Bartoli was playing her fifth straight Eastbourne semifinal but had never before progressed to the final.
She broke to lead 2-0 when Stosur netted a forehand and fought off a break point in the next game.
Bartoli broke again to lead 2-1 in the second set when Stosur made another forehand error and then dominated with her more aggressive play and fewer unforced errors.
Hantuchova led 3-0 after breaking in the second game, but Kvitova broke back in the fifth game and Hantuchova received treatment when leading 4-3.
She held a set point at 6-5 in the tiebreaker before Kvitova edged through on her fourth set point. The Czech broke to lead 2-0 before Hantuchova retired four games later.