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2016 US Open scores and bracket: Serena Williams earns historic 307th Grand Slam match win

Williams now has more wins in Grand Slams than any woman in the Open Era.

Robert Deutsch-USA TODAY Sports

Serena Williams posted her 307th career Grand Slam victory on Saturday, taking down Sweden's Johanna Larsson in straight sets, 6-2, 6-1. It was a historic win, and Williams earned it in the dominant fashion we're all used to. The total surpassed Martina Navratilova for the most Grand Slam victories in women's tennis history.

It also tied Roger Federer for the most all time by any competitor. Federer has been dealing with injuries of late and is not participating in the US Open, so he'll have his work cut out for him staying ahead of Williams, who is still the world No. 1 player.

Williams advanced to the Round of 16 with her win on Saturday. She entered the US Open with her No. 1 ranking under fire, with all of Angelique Kerber, Agnieszka Radwanska and Garbine Muguruza potentially able to grab the ranking. Williams was defending more points at the event than the rest of them as well, which hurt her chances at holding on.

But Muguruza has already been eliminated, so she isn't a threat. Williams has also progressed far enough that Radwanska would both have to eliminate Williams if they face off in the semifinals and beat Kerber in the finals to earn the ranking. Kerber is still a live threat at taking the ranking, but Williams' play on Saturday was excellent and she is certainly the woman to beat.

Radwanska punched her ticket into the Round of 16 on Saturday as well, downing No. 25 Caroline Garcia in straight sets, 6-2, 6-3. Radwanska has played great tennis at the US Open, but she has never beaten Williams in singles competition and the two could meet in the semifinals as they were drawn into the same half of the tournament.

Simona Halep, the fifth seed, and Carla Suarez Navarro, the No. 11 seed, also advanced past the third round on Saturday.

Andy Murray was the top men's seed in action on Saturday, and he had his hands full with unseeded Paolo Lorenzi. Murray was pushed to a tiebreak in the first set, but ultimately took it before Lorenzi charged back to take the second set. But from there, Murray dug deep and took the next two sets and punched his ticket to the Round of 16.

Murray is the top competition for Novak Djokovic, who made it to the Round of 16 without having to play more than four full sets thanks to injuries to his second- and third-round opponents. Murray needs to stay off the court as much as possible, because Djokovic has the edge over Murray in most cases. He'll need to mitigate every advantage he can.

Below is a list of results from Saturday's singles matches that include seeded players. If a match doesn't have a score, it is not yet complete and will be updated when it's finished.

Men's Singles results

No. 2 Andy Murray def. Paolo Lorenzi, 7-6(4), 5-7, 6-2, 6-3
No. 3 Stan Wawrinka vs. Daniel Evans
No. 6 Kei Nishikori vs. Nicolas Mahut
No. 8 Dominic Thiem def. Pablo Carreno Busta, 1-6, 6-4, 6-4, 7-5
Juan Martin Del Potro def. No. 11 David Ferrer, 7-6(3), 6-2, 6-3
No. 14 Nick Kyrgios vs. Illya Marchenko
No. 21 Ivo Karlovic vs. Jared Donaldson
No. 22 Grigor Dimitrov def. Joao Sousa, 6-4, 6-1, 3-6, 6-2

Women's Singles results

No. 1 Serena Williams def. Johanna Larsson, 6-2, 6-1
No. 4 Agnieszka Radwanska def. No. 25 Caroline Garcia, 6-2, 6-3
No. 5 Simona Halep def. No. 31 Timea Babos, 6-1, 2-6, 6-4
No. 6 Venus Williams vs. No. 26 Laura Siegemund
No. 10 Karolina Pliskova def. No. 17 Anastasia Pavlyuchenkova, 6-2, 6-4
No. 11 Carla Suarez Navarro def. No. 19 Elena Vesnina, 6-4, 6-3

Tomorrow

The Round of 16 begins, which means Djokovic and Rafael Nadal will both be in action for the men. Kerber will also be playing, and she's set to face the tough Petra Kvitova, the 14th seed. Madison Keys, the eighth seed for the women, will be facing the surging Caroline Wozniacki.

On Sunday, play begins at 11 a.m. ET. Television coverage of the day will be handled exclusively by ESPN2, beginning at 11 a.m. and running through 11 p.m. Live streams will be available online at WatchESPN.

Keep up with the US Open men's bracket, schedule and results here. The women's bracket can be found here.