Serena Williams continued her hunt for a record seventh US Open title with a straight-sets win on Thursday as Andy Murray crashed out in the second round at Flushing Meadows.

Williams, the tournament's third seed, dispatched unseeded Russian Margarita Gasparyan 6-2, 6-4 under the roof of a near-empty Arthur Ashe Stadium on a wet New York evening.

The 38-year-old closed out the first set with ease before a slight wobble in the second when she was broken twice by Gasparyan, before progressing into the third round.

"I'm just happy to get through it and try to focus on the next round," said Williams, who will take on 2017 champion Sloane Stephens in the last 32.

Williams is seeking a record-equalling 24th singles Grand Slam title at a subdued, spectator-free Billie Jean King US National Tennis Center in New York.

A tournament victory next week would also see her break away from Chris Evert, on six titles, as the most decorated US Open champion of the women's game in the modern era.

Williams' chances have been improved by the absence of several top players, included top-ranked Ashleigh Barty and Simona Halep, over coronavirus fears or injury.

She was handed a further boost on Wednesday when top seed Karolina Pliskova tumbled out of the tournament.

The Czech was stunned in straight sets by France's world number 50 Caroline Garcia.

Williams' American compatriot Sofia Kenin, the number two seed, continued her impressive form this year with a straightforward 6-4, 6-3 victory over Canadian Leylah Fernandez to progress into the third round.

The reigning Australian Open champion Kenin is yet to drop a set at Flushing Meadows as she bids for her second Grand Slam title of the year, and of her career.

"I feel like I found a groove. I'm really focused on every shot," said the Moscow-born player who will take on 27th seed Ons Jabeur of Tunisia in the next round.

In the men's draw Andy Murray, slumped to a 6-2, 6-3, 6-4, defeat against a dominant Felix Auger-Aliassime.

The 15th seed Canadian smashed 24 aces and 52 winners in a one-sided affair that saw Murray muster just two and nine respectively.

"I just felt like everything was coming in, my toss, my rhythm. Everything was going well through the whole match," said Felix Auger-Aliassime.

- Pironkova return -
In early men's matches, second seed Dominic Thiem celebrated his 27th birthday with an easy straight-sets win against India's Sumit Nagal.

The Austrian triumphed 6-3, 6-3, 6-2 against Nagal, who became the first Indian man since 2013 to reach the second round of a Grand Slam.

Thiem will play 2014 US Open champion Marin Cilic for a place in the fourth round after the Croatian advanced in four sets against Slovakia's Norbert Gombos.

"He's one of the big champions of the last decade, Thiem said of Cilic. 

"It's not a guy I want to face in the third round."

Third seed and beaten finalist last year Daniil Medvedev made light work of Australia's 116th-ranked Christoper O'Connell, easing into round three 6-3, 6-2, 6-4. 

Elsewhere, sixth seed Italian Matteo Berrettini brushed aside France's Ugo Humbert 6-4, 6-4, 7-6 (8-6) while Spaniard Roberto Bautista Agut progressed against Serbian Miomir Kecmanovic.

In the women's competition Thursday, Tsvetana Pironkova, returning after a lengthy time away from the game following the birth of her son, advanced at the expense of Garbine Muguruza.

The unseeded Bulgarian knocked out the 10th Spaniard 7-5, 6-3 in 1hr 21 min.

"Coming from three year of absence on the tour, you always have your doubts. Right now my results actually make me really happy because it shows that I did the right things preparing for this comeback," said Pironkova.

Seventh seed Madison Keys of the USA also progressed, making light work of Spain's Aliona Bolsova 6-2, 6-1, while Stephens easily overcame Belarusian Olga Govortsova 6-2, 6-2.

British ninth seed Jo Konta became another high-ranking woman to be sent packing, losing in three sets to Romania's Sorana Cirstea after going a set ahead.