Rafael Nadal was tested once again at the 2018 U.S. Open at Flushing Meadows, as Nikoloz Basilashvili claimed the third set before falling to defeat on Sunday.

The Spaniard was involved in a gruelling battle against KarenKhachanov in the third round, and the No. 1 seed had to produce moments of magic to win this match.

Nadal prevailed 6-3, 6-3, 6-7 (6), 6-4 as his campaign continues into the quarter-finals in New York.

Serena Williams made it to the next round after overpowering Kaia Kanepi at Arthur Ashe Stadium.

The legend won the opening set without dropping a game before Kanepi extended the match by winning the second.

Williams completed the victory, 6-0, 4-6, 6-3, to reach the last eight.

There were also victories for Dominic Thiem and Karolina Pliskova, who defeated Kevin Anderson and Ashleigh Barty, respectively.

Here's a selection of early results and evening schedule for Sunday's major encounters:

Arthur Ashe Stadium

(1) Rafael Nadal def. Nikoloz Basilashvili 6-3, 6-3, 6-7 (6), 6-4

(17) Serena Williams def. Kaia Kanepi 6-0, 4-6, 6-3

(3) Sloane Stephens def. (15) Elise Mertens 6-3, 6-3

(3) Juan Martin del Potro def. (20) Borna Coric 6-4, 6-3, 6-1

Louis Armstrong Stadium

(9) Dominic Thiem def. (5) Kevin Anderson 7-5, 6-2, 7-6 (2)

(8) Karolina Pliskova def. (18) Ashleigh Barty 6-4, 6-4

(11) John Isner def. (25) Milos Raonic 3-6, 6-3, 6-4, 3-6, 6-2

Sunday Recap

Nadal has truly been put through his paces in this year's competition, but the Spanish icon has been equal to the challenge as he moves through the gears.

The opening two sets were straightforward for the top seed, firing off the sets, 6-3, 6-3.

However, Basilashvili was far from finished, and the Georgian upped his output to exert physical pressure on his illustrious opponent.

The 26-year-old claimed the third via a tiebreak, 8-6, and Nadal temporarily appeared in slight trouble.

Once again, the Spaniard reacted as he did against Khachanov, who gave him a huge test in his previous match.

Nadal claimed the final set 6-4 and extinguished the threat of a shock exit.

Basilashvili showed plenty of depth as he hit an astonishing 56 winners, but Nadal was dominant on his own first serve, winning 75 per cent of points.

The U.S. Open highlighted the winning moment on Twitter:

Williams was in complete control early on against Kanepi, and a lightning-quick first set saw the legend win the opener 6-0.

Kanepi was caught in Williams' headlights, but to her credit, she recovered her composure to stop her opponent's charge.

The Estonian stunned the Flushing Meadows crowd as she won the second set 6-4, and Williams was bemused as she sat in her chair.

However, the American icon had no intention on leaving the door open for the 33-year-old, and she slammed it shut by taking the third and final set, 6-3.

Williams was dominant with the serve as she aced 18 times, and she is a serious threat once again after her recent return to the circuit.

No. 9 seed Thiem booked his place in the next round as he eliminated Anderson.

Anderson was expected to go deeper into the tournament as the No. 5 seed, but the South African couldn't stop the Austrian.

Thiem took the victory in straight sets, winning 7-5, 6-2, 7-6 (2) in two hours, 37 minutes.

Pliskova continued to show her fine form as she attacks the latter stages, and she was a clear winner in straight sets against No. 18 seed Barty.

The former world No. 1 was in no mood to concede any territory to her opponent, and she skipped to a simple 6-4, 6-4 victory.

Sloane Stephens also had a relatively easy trip to the quarter-finals with her straight-sets victory over Elise Mertens. The American didn't provide her opponent with many chances to beat her on the serve, getting 83 per cent of her serves in play while winning 73 per cent of those first serves.

She was just as difficult to serve against, leaving Mertens with few options in the 6-3, 6-3 loss.

Perhaps the best match of the day belonged to John Isner and Milos Raonic, with the former coming away with a five-set victory. Isner was not only good with his serve, but he avoided mistakes against an obviously talented opponent.

The No. 11 seed had 20 aces with just one double-fault, plus 56 winners with 25 unforced errors. This helped Isner earn a trip to the quarter-finals at the U.S. Open for just the second time in his career.

All stats via U.S. Open's official website.