Radwanska actually looked on her way to a straight set win after about two hours. Having already taken the first set in a tie-break, she seemed in total control of the second set tie-break as well, going up 4-0 - Williams reeled off seven straight points to take it though, so on to a third set they went.
Again Radwanska built a hefty lead, going up 5-1, and again Williams stormed back, closing the gap to 5-4. But a few last unforced errors crept in at the worst of times, and with one last backhand into the net the No.30-seeded Williams sealed her fate - game, set and match Radwanska, 76(5) 67(4) 64.
"It's an amazing feeling to beat her here," Radwanska said. "I was talking with Aga about playing her, and I've also watched a couple of their matches, so I was prepared for this match. And I also knew she is a great fighter, so I made sure I was focusing really hard at the end to close the match out."
Curiously, Williams actually had the better numbers in the match - her -8 differential of 58 winners to 66 unforced errors was four better than Radwanska's -12 differential of 28 winners and 40 unforced.
"I was just in a really big hole," Williams said. "It's definitely not the place you want to be in the third set, but I just tried to stay positive and keep fighting back. And I have to say she played really well. She didn't make a lot of unforced errors, she kept bringing a lot of balls back and competed well.
"I definitely have to give her a lot of credit for that."
Williams' lead-up to the French Open was thin - since reaching the semifinals of Charleston in early April she only played one event, Rome, and fell first round. She missed Madrid with a back injury.
"My preparation was extremely unideal," Williams commented. "I've definitely been struggling. But I just wanted to come here and try to go out there and play. I think my movement is awesome, but I just haven't played any matches and just haven't hit any serves, and it's hard to be perfect in the first match back. But I think there were periods where I found some rhythm, and some where I didn't. I can't really serve very hard, but I'm getting better. I just ran out of time to get better for this tournament.
"I want my serve back - I'm going to try to get it back for Wimbledon."
Williams was also asked if she ever considered this to be her last match at the French Open.
"If it's the last match, I'll let you know," she replied. "That's pretty much how it works."
The former World No.1 - who returned to the tour after a seven-month illness lay-off last March and has already been back in the Top 20 for a time - then reminded everyone how inspiring she is.
"It's obviously disappointing to lose - it's not what anyone is going for out here. But I'm strong and I'm a fighter. What I've gone through is not easy. And I don't think I'm just playing for me now, I think I'm playing for a lot of people who haven't felt well. So for me today it's a big positive to be able to play for three hours. And I'm constantly finding ways to get better and feel better out there on the court.
"I would never give up. Obviously at some point everyone has to retire, but I feel like I have to give myself a chance to continue working on feeling and playing better. I wouldn't just give up because it was difficult. That's not me. My thing is I'm going to keep trying. You know, I had a very challenging year last year, but I had many successes as well. I'm continuing to look forward to more success."
Next up for Radwanska is German qualifier Dinah Pfizenmaier, who won a tight first set against Mandy Minella then cruised for a 75 61 victory. Radwanska and Pfizenmaier will be playing for the first time.