"She was playing unbelievable tennis,'' Radwanska said of Li.
"I'm just very happy to have got through, even when I was struggling a little bit in the third set, I'm still very, very happy to be in the semi-final.''
With world No.1 Williams, Victoria Azarenka, Maria Sharapova and Sara Errani all out in the first week, Li and Radwanska were the highest-ranked players left.
The contest was punctuated by lengthy rallies, with Radwanska throwing in her trademark array of deft lobs and soft drop shots that mark her out among the booming baseliners of the women's game.
In the first set, Radwanska and Li fought a big tussle for the eighth game, which Li held for 4-4. The momentum was now with the Wuhan right-hander and she duly broke serve in the next game to serve for the set.
However, Radwanska was able to stave off set point in a net duel and fought off three further set points, eventually breaking to level the scores.
That swung the momentum in the Pole's favour and she won the tie-break to seal the 65-minute set.
Radwanska quickly broke for a 2-1 lead in the second set.
Li fashioned a break point right when she needed it, at 4-3 down, and won it to level the set at 4-4. The 31-year-old broke again to take the set.
Radwanska called for the trainer at the break and had her right thigh heavily taped up, while Li studied her notes.
In the third set, Radwanska broke for a 2-0 lead before the rain came again.
With the roof closed, the Pole broke again for a 4-1 lead and then held serve to leave Li on the brink.
The Chinese held off match point twice on her serve and won the game.
With Radwanska serving for the match, Li fashioned three break points but blew them all.
Li then managed to cling on repeatedly before her luck eventually ran out on Radwanska's eighth match point.
-AAP
