In the first serve neither player could hold serve and Na just edged it 7-5.
She went down 2-0 in the second but responded by dropping just one more game on her way to a 7-5 6-3 win.
Read how the action unfolded with Sports Mole's live commentary.
12.02amHello all and welcome to our first match of this quarter-final stage.
12.03amIt's a very long walk out onto the court. And a quiet one, for the players. They both look focused.
12.05amIt's the 10th time these have met, with Li currently 5-4 up. They are seeded fourth (Radwanska) and sixth, so there's nothing to choose.
12.06amToday we have four matches, one after the other. Two from the men's and two from the women's.
12.08amFollowing this one will be the all-Spain clash between David Ferrer and Nicolas Almagro at approximately 2am, Ekaterina Makarova vs. Maria Sharapova at around 5am and Novak Djokovic vs. Tomas Berdych not before 8.30am
12.10amI would expect this one will go to three sets, but you never know if one of them comes out firing.
12.12amWe're off here, Li to serve. Let's hope for a competitive game now at this stage of the tournament.
12.14amBig serve spinning out wide that is not returned gives
Li a game point.
Li a game point.
12.16amBig baseline rally goes Radwanska's way, as you might think. Na eventually went for the winner but put a backhand into the net. Radwanska will play those points all day long.
12.18amAt advantage another patient rally from Radwanska ends with Li hitting a forehand wide.
12.20amDeuce number four..
Li 1-0* RadwanskaWell, if all the games are as long as that one we'll be here until the weekend. Li saves two break points in that one and finally holds a 12-minute game with a couple of volleys.
12.26amThis time Li comes out on top of a big rally, with a fantastic forehand across the court, finishing right in the corner.
12.27amThen puts a simple volley wide and it's 15-15 instead of 0-30.
12.29amThe second game also goes to deuce, after Radwanska goes just long with a tricky baseline lob.
Li *1-1 RadwanskaHowever, the Pole takes the game and we're with serve at the moment.
Li 1-2* RadwanskaBREAK! I think it's quite rare that Radwanska doesn't get a point on her opponent's service game, although she was helped by some poor shots from the Chinese in this game. Radwanska nets a simple backhand on first break point, but Na returns the favour on the second one and first blood the Pole.
12.38amAlso rare is a foot fault, but Li was given one in that last game. It was very close, in her defence. A little picky.
12.39amGreat response from the Chinese. Radwanska comes to the net but Li passes her down the backhand line for 0-30, great shot.
12.40amA double fault from Radwanska and three break points for Li.
Li *2-2 RadwanskaBREAK! Radwanska gave that up surprisingly easily, but it was much more aggressive from Li as she hit the corners a few times.
12.44amNa goes from the sublime - a superb backhand down the line - to the poor - an overhit forehand - to gift another break point to the Pole.
Li 2-3* RadwanskaBREAK! Li saves it but Radwanska pings the ball into the corner forcing the Chinese into a net shot to set up another. Radwanska breaks again, the third straight in the match.
Li *3-3 RadwanskaBREAK! Another game, another battle. That's the fourth break in a row and once again we're back on serve. Or is that back on break?
12.52amLi starts with her first double fault, after twice going long with the serve.
12.54amThere is a fascinating story in the boys' draw, with deaf teenager Lee Duck-hee reaching the second round. Here's what he had to say.
12.55amI think every game apart from one so far has been at 30-30. Li wins a good rally with a forehand winner to reach 40-30
Li 4-3* RadwanskaA hold of serve! Well done Li, who responded well in that game to put a little pressure back on the Radwanska serve.
12.58amLi dominates a fantastic rally. Radwanska gets to almost everything, however, but Li finishes the point with a big backhand winner.
12.59amWhat a fantastic point. After a baseline rally, Radwanska tries a sublime drop shot, which Li reach only for the Pole to flick it back over her head and right on to the line.
Li *4-4 RadwanskaRadwanska wins the game with her first point in a comfortable hold.
1.02amThree break points for Radwanska...
Li 4-5* RadwanskaBREAK! Too good from Radwanska in that rally. A 26-shot rally ends with Li going long after typical accurate hitting from the Pole. She will now serve for the set.
1.05amLi responds with a booming forehand for 0-30. Maybe this set has another twist?
1.05amFantastic passing forehand this time, and 0-40.
Li *5-5 RadwanskaBREAK! It's happened again. Li breaks Radwanska back for the third time and this one was to love. This one's got to be ending in a tie-break.
1.08amNow Radwanska 0-30 up. Really bizarre flow to this one, both players are far better off-serve.
1.10amLi battles back to 30-30 after a good rally ends with a controlled smash at the net.
1.11amOh, my. What an incredible cross-court backhand Li has just pulled off. That's one of the best I've seen in the past week and a half.
Li 6-5* RadwanskaLi hangs on after deuce and Radwanska now to serve to take this into a breaker.
1.16amAt 15-30 Li goes for the pass after a weak Radwanska smash, but it's wide.
1.17amTerrible decision for a drop shot from the Pole allows Li to win off the forehand for set point.
1.17amRadwanska saves it with a fantastic piece of net play. Deuce. Again.
Li *7-5 RadwanskaSET! Li makes no mistake with her second set point, putting Radwanska on the defensive and finally finishing with the Pole netting.
1.20amIt was a topsy-turvy set and could have gone either way. It went the way of the Chinese after she finished the set much stronger. Really interesting tennis, if not of the highest quality.
Li 7-5 0-1* RadwanskaBREAK! Radwanska comes out for the second set on the attack and moves 0-40 ahead. Na finishes off with an atrocious backhand and it's the perfect start for the Pole.
1.24amNow she's 30-0 up on her serve. Li yet to win a point in this set.
Li 7-5 *0-2 RadwanskaThe set loss has awoken Radwanska. Eight points from eight go her way to start this set and she's racing ahead without being brilliant.
1.27amLi finally gets a point in the set with a good volley winner at the net.
Li 7-5 1-2* RadwanskaLi is now up and running. She responds well from two games down and finishes off her next serve with an ace out wide.
1.31amShe's now 0-30 up in her effort to break back.
1.33amTwo set points for Li after a good advancement to the net and a backhand winner.
Li 7-5 *2-2 RadwanskaBREAK! Indeed she does break back. After losing the first eight points of the set, Na has now won six of the next eight. This odd game continues.
1.35amLi has just submitted her entry for the worst fault competition. That one didn't even bounce in court, let alone the serving box. She responds to take the point for 30-0.
Li 7-5 3-2* RadwanskaRadwanska battles back but Na has recovered superbly from her poor start to go ahead in the set for the first time.
1.39amLi races into a 0-30 lead and she's bossing things on court.
1.39amThree set points earned with a gloriously confident volley after a late arrival at the net. Wow.
Li 7-5 *4-2 RadwanskaBREAK! She needs just the one! A backhand return down the line and Radwanska doesn't even move for it. Incredible few games from Li.
Li 7-5 5-2* RadwanskaIt's nine points in a row for Li before she nets, but a routine service game for her moves her to within a game of the semi-finals.
Li 7-5 *5-3 RadwanskaRaswanska does all that she can do by holding serve relatively routinely. The ball is now in Li's court to win this. Quite literally.
1.50amRadwanska goes up 0-30 but Li responds with another brave advancement and volley. She could have been staring down the barrel of a break there.
1.51amShe is now after going long... Two break points.
1.53amFantastic, huge hitting from Li drags her back to deuce. Huge point that was.
1.53amMatch point Li.
Li 7-5 6-3 RadwanskaGAME, SET AND MATCH! Radwanska goes long and Li advances! She played impeccably at 2-0 down in that second set but she was incredibly strong mentally and takes it in straight sets. She's still to drop one and is improving game by game.
1.57amThat wraps up the coverage of the first quarter-final. Join me shortly for Ferrer vs. Almagro.