It was the Pole who made the first breakthrough, taking down Li's serve in the third game of the match thanks to a few costly errors from the sixth seed.
That kicked Li into action, as she began to play much more aggressively and was rewarded with a break back in the next game.
The pair exchanged breaks once more before Radwanska edged back in front at 5-4. However, the topsy-turvy nature of the set continued as she relinquished the advantage once again in the next game.
The seventh break in the first set proved to be the crucial one, with Li taking it 7-5.
Radwanska responded well at the start of the second set, breaking at the first time of asking before going on to consolidate for the first time in the contest.
Li then took control, storming back to win six straight games and put herself within a game of victory. Radwanska looked completely shell shocked as her opponent put on a tennis masterclass.
The fourth seed did threaten to claim one of the breaks back as the 30-year-old served for a place in the last four, but Li's resolve was there for all to see.