And that answers the question as to who Serena Williams will face next. The defending champion will meet Spanish 18th seed Carla Suarez Navarro for a place in the semi-finals.
Serena Williams - Sloane Stephens
US Open women - 2 September 2013
US Open – Follow the Tennis match between Serena Williams and Sloane Stephens live with Eurosport. The match starts at 01:00 on 2 September 2013. Our live coverage lets you follow all the key moments as they happen.
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WILLIAMS 6-4 6-1 - GAME, SET & MATCH! A service winner from Williams brings up three match points. Stephens saves the first with a forehand winner while Williams squanders the second with a double fault. But Williams books her place in the quarter-finals of the US Open at the third attempt when Stephens nets a forehand.
WILLIAMS 6-4 5-1 - BREAK! Stephens finds herself staring at another two break points as she runs out of steam in this second set. But Williams only needs the one and will serve for the match after Stephens pulls a cross court backhand across court.
WILLIAMS 6-4 4-1 - Williams is racing away with this second set now as she holds without trouble when Stephens nets a forehand. The older American drew her opponent up to the net on the penultimate point before putting a forehand volley passing shot down the line for Stephens to chase. The younger American actually got there but could not return the ball and Williams is potentially just two games away from the win now.
WILLIAMS 6-4 3-1 - BREAK! Stephens pulls a backhand wide across court to allow Williams to level at 30-all. She sneaks ahead with a forehand winner before a double fault sees Williams level at deuce. The defending champ then batters a cross court forehand return winner to earn herself a break point before sealing it with a series of brutal forehands on to the baseline which eventually draws the netted forehand from Stephens.
WILLIAMS 6-4 2-1 - Stephens over-runs a smash down the centre of the court from Williams, obviously thinking her opponent was going across court. She pretty much runs into the ball and Williams has another love service hold to her name.
WILLIAMS 6-4 1-1 - A terrific half-volley backhand across court from Stephens helps her bring up game point from 30-all before she secures her easiest service game of the match so far to stick with Williams early in this second set.
WILLIAMS 6-4 1-0 - Another brutal rally from Stephens ends with her seventh forehand winner, on the short ball up at the net. It sees her level at 30-all before a netted short forehand from Williams hands Stephens are early break point in this second set. An eighth forehand winner denies Williams on a game point but Serena does hold at the second attempt with an error from Stephens.
WILLIAMS 6-4 - SET! A nervy forehand long from Stephens hands Williams a first set point. But the 15th seed produces some gutsy hitting to save it, peppering the baseline and eventually drawing the error (a forehand long) from Williams. Stephens fails to take advantage of a game point and then hands Serena a second set point with a forehand long. A cross court forehand winner saves it but Williams gets a third chance and this time Stephens hits long to concede the opening set.
WILLIAMS 5-4 - Another brutal point from Stephens as she wins yet another longer rally, hitting consistently across court on the forehand before going down the line and drawing the lob long from Williams. But Serena still holds for the loss of just the one point when Stephens's cross court forehand is called just wide. Stephens will serve to stay in the set after the change of ends.
WILLIAMS 4-4 - Stephens lets out a little squeal of frustration when she pulls a forehand wide across court. She levels at 30-all but then nets another forehand to gift Williams a point to re-establish her break lead. Stephens saves it though with a forehand winner before going on to hold at the second attempt when Williams nets a forehand.
WILLIAMS 4-3 - BREAK! A huge inside out forehand winner right out of the centre of the racquet from Williams sees her go 30-15 ahead before a smash winner from Stephens levels it. A double fault from Williams then hands Stephens a break back point before a second consecutive double fault hands the younger American the immediate break back. Incredible stuff.
WILLIAMS 4-2 - BREAK! Stephens hesitates up at the net, putting her forehand volley into the net as a result to hand Williams two break points. But the world number one only needs the one as she rattles a forehand winner over the net.
WILLIAMS 3-2 - A second love service game from Serena is sealed when Stephens tracks out to her left only to pull her backhand wide across court.
WILLIAMS 2-2 - A couple of loose forehands from Stephens, the second pulled wide across court, help Williams on her way to a first break point. Stephens saves it with a forehand winner before doing the same again a couple of points later on a second break point. That was an incredibly brutal inside out forehand from Stephens, Williams grunting with the effort just of blocking the previous shot back! Stephens saves two more when Williams hits long and Stephens goes on to hold after 9 minutes!
WILLIAMS 2-1 - Williams looks to be racing through a second love service game after Stephens just misses a change-of-direction forehand down the line. The world number one slaps down a double fault to squander her first game point but then produces her 396th ace of the year to seal it for the loss of just the one point.
WILLIAMS 1-1 - Immense hitting from both players very early on that is already drawing gasps from the crowd on account of the power. Stephens slaps down a double fault to allow Williams to level at deuce before drawing the older American into two lengthy rallies, Williams's forehand breaking down on the first sailing long before a bakchand goes long on the second.
WILLIAMS 1-0 - Williams keeps Stephens waiting after the 20-year-old comes out for the start of the match, but her opening service game is anything but slow as she races through the hold to love with a series of booming serves.
It's Labor Day weekend, it's 4.20pm on the middle Sunday of the US Open and it's an all-American fourth round clash. Serena Williams v Sloane Stephens.
Stephens has won the toss and opted to receive first, hoping for a few nerves early on from Williams.
These two have faced each other twice before, both times this year, with Williams winning in straight sets in Brisbane before Stephens hit back just two weeks later in the Australian Open quarter-finals when the youngster won in three sets.
Coming up next on Arthur Ashe will be defending champion and world number one Serena Williams taking on the woman touted as the future of American tennis, Sloane Stephens.