However, Li then rattled off five straight games and saw off two break points when she served for the match at 5-3 to claim her sixth win in 10 meetings with Radwanska.
Radwanska had been on a run of 13 straight wins, including 26 sets unbeaten, after claiming tournament wins in Auckland and Sydney.
Li will face the winner of Tuesday's all-Russian quarter-final between world number two Maria Sharapova and Ekaterina Makarova in the last four.
Li, a 2011 Australian Open finalist, is now into her first Grand Slam semi-final since she won the French Open in 2011.
The world number six, formerly coached by her husband Jiang Shan, praised the input of her new coach Carlos Rodriguez.
"I think it was pretty good for me and my husband. It is much easier for our life, we don't have to shout at each other on the court and also off the court," she joked.