It was the 27-year-old's third straight sets win out of three played against a player ranked one place above her in the world.
Stosur also reached her first final since the 2010 French Open almost a year ago.
The sixth seed got off to a flying start and broke Li in the opening game, working the Chinese wide to her backhand and forcing a short defensive return before steaming up to the net and powering away a forehand winner.
Stosur forced a set point on the fourth seed's serve at 5-3 but a deep first serve gave Li a short return to put away.
A series of deep crosscourt backhands setting her up for a forehand winner from close to the net saw Li fend off another set point soon after before she held serve.
That proved a vital hold as in the next game Li forced a break point and levelled up at 5-5 when Stosur went wide with a backhand.
The first mini-break in the tie-break went Li's way when she brought Stosur up to the net with a drop shot and then rasped a backhand pass crosscourt.
But she gave it up immediately with a double fault.
Li brought up a set point with a forehand winner down line but could not take it when she put the same shot into the tramlines on the next point.
Stosur was not so generous when she was presented with a set point moments later, hitting a powerful serve out wide and following it up with a forehand winner.
The world number seven got off to quick start in the second set as well as Li double faulted on break point in the second game.
And the Chinese player's game crumbled from there as Stosur cantered through the rest of the set.
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