Having seen compatriots Jerzy Janowicz and Lukasz Kubot make the last eight of the men's draw on Monday, the pressure was on Radwanska on Monday and the fourth seed delivered after a lengthy clash on Centre Court which she won 7-6 (7/5) 4-6 6-2.
Radwanska, runner-up last year, saved four set points in the opening set and she also had to contend with thigh problems during the match.
Radwanska, who is bidding to win her first grand slam, admitted afterwards that she was struggling to cope with her injury through the latter stages of Monday's quarter-final win.
"It's because of too much tennis over the last few days," Radwanska told the BBC.
"That's why I was struggling. But it's a good problem. I will keep going and try my best."
Radwanska is looking forward to playing Serena Williams' conqueror Sabine Lisicki in the semi-finals on Thursday.
"I am very to happy go through," said Radwanska, who is the highest-ranked player left in the tournament.
"Sabine and I know each other so it will be a big challenge for me to play her on grass."
"It's always good to play people you have come against as juniors.
"This is the first time we have played on grass. She must be playing well if she beat Serena."
Radwanska, who is aiming to become the first Pole in history to win a grand slam singles title, started poorly on Tuesday as Li broke immediately.
The Pole hit back straight away, however, when her Chinese opponent went long with a backhand.
Li then gained the upper hand, taking the ninth game to move 5-4 ahead. Serving for the set, nerves got the better of the Chinese as she wasted four chances to win the game and Radwanska broke, setting up a tie-break.
Radwanska, seeded fourth, earned two set points in an error-strewn breaker and she took the first one available to win the showdown.
After a brief rain delay, Radwanska wasted little time on stamping her authority on the second set, breaking early on when Li netted.
Li then converted her first break point of the set with a smash.
Radwanska had a chance to break back straight away, but this time Li kept her cool and opened up an angle to send down a forehand winner.
Radwanska then buckled under pressure, losing the set 6-4 after being broken at the worst possible time.
After almost 10 minutes of treatment on her right thigh, Radwanska returned to action wearing heavy strapping, but it was clear from the off that the injury was not hindering her.
The Pole broke Li to move 1-0 up before rain brought play to a halt. The players returned after 25 minutes and Radwanska remained on top.
The 24-year-old missed four chances to break again, but took the fifth when Li sent a forehand wide following a tense rally.
Li was made to serve to stay in the set, but she struggled to land her first service and had to save two match points.
Radwanska had some further treatment, this time to her left thigh.
Serving for the match, she was then hit by a bout of nerves.
The Pole had to save three break points and she spurned five more match points, before eventually booking her place in the semi-finals after two hours and 43 minutes on court.
Poland will definitely have a man in the semi-finals for the first time in 33 years after Janowicz and Kubot were paired together in the last eight.
Radwanska is happy that Poland's players are faring well in the majors.
"I think it's a really huge thing for Poland," Radwanska said. "I don't know why we're doing well all of a sudden. I think we all like grass.
"I have a day off tomorrow [Wednesday] so I will go and watch the guys' match. I love them both."