And that would be the No.1-seeded Williams, who had to battle two hours and 14 minutes to make it past Anabel Medina Garrigues, dropping the second set at love and coming within two points of defeat serving at 4-5, 15-30 in the third but eventually coming out on top against the Spaniard, 63 06 75.
"It was definitely a battle," Williams said. "I obviously didn't do much in the second set, which gave her a lot of confidence to play better. And then I thought she played really well after that in the third.
"I definitely want to cut back on my unforced errors. I had a lot of them today. Also I went for a lot more today than I have been in my past few matches. So I think I'm going to go back to the way I have been playing and being more calm and not making as many unforced errors as I did out there today."
And on the love set? "I wasn't really there, my feet weren't moving - I don't know what happened," she said. "To turn it around I got up earlier on the changeover and started doing high knees and just stretching and doing anything to try to get my intensity back up to where it needed to be.
"This second set is a good reference. I can show a lot of juniors what not to do."
Medina Garrigues joins some elite company - it was just the seventh time in her entire career that Williams had lost a set at love, the first six players to do it being Alexia Dechaume-Balleret, Mary Joe Fernandez, Jelena Jankovic, Justine Henin, Patty Schnyder and most recently Venus Williams.
"As the second set was going on I was thinking, 'It might happen,'" Medina Garrigues said afterwards. "I was wondering how many sets Serena has lost at love - I don't think it's many. It's true she let her level drop a little bit in the second set, but I had to win it, too, and I did. And there it will stay for history.
"And then I was also two points from winning at 5-4 in the third set. But she did an ace, and I couldn't do anything. It's a pity I lost today, but she's the No.1 in the world because of those things."
The No.2-seeded Sharapova followed Williams onto center court and moved past Kaia Kanepi, 62 64.
"I was just happy to get past the quarterfinals - I feel like I've been stuck there in this tournament," Sharapova said. "I faced a really good clay court player today. A lot of her success has come on clay. I faced her at the French Open last year, where she had really good wins, so I know that she's capable. I was just really determined today, and I'm happy I was able to win with that type of scoreline."
Awaiting Sharapova in the semifinals is No.16 seed Ana Ivanovic, who broke serve six times and needed just 57 minutes to take out No.6 seed Angelique Kerber in the last match of the day, 63 61, an upset on paper but not based on the pair's history - Ivanovic is now 3-0 lifetime against Kerber.
Sharapova leads Ivanovic in their head-to-head series, 6-2, and has won their last five meetings in a row - their only 2013 meeting was a three set marathon in Stuttgart last month, however.
And so the battle for the No.1 ranking lives on, with Sharapova needing to do one round better than Williams to take the top spot - so if Williams loses in the semifinals, Sharapova will take it by just winning her semifinal; if Williams makes the final, Sharapova will take it by beating her in that final.