The American, who has been struggling with a shoulder problem of late, breezed past the Rio 2016 Olympic doubles gold medallist 6-3, 6-3 to reach the second round.

The top seed showed little sign of the injury which has hampered her build-up to the tournament, the final Grand Slam of the year, to book a meeting with compatriot Vania King.

“I'll have to wait until tomorrow to see, I haven't been able to play that much since Wimbledon,” Williams said.

“I love coming out here in front of this New York crowd, it's super special.”

Sister Venus was also able to progress to round two as she saw off the challenge of Kateryna Kozlova of Ukraine in three sets, 6-2, 5-7, 6-4, despite amassing a total of 63 unforced errors.

Elsewhere in the women’s draw, Poland’s Agnieszka Radwanska, seeded fourth, thrashed American Jessica Pegula 6-1, 6-1, while fifth seed Simona Halep of Romania was also in good form as she beat Belgium’s Kirsten Flipkens 6-0, 6-2.

In the men’s competition, Olympic champion Andy Murray of Britain ensured a safe passage into the second round with a dominant win against Lukas Rosol of the Czech Republic.

Murray, the current world number two, is considered one of the favourites for the event with main rival Novak Djokovic suffering a rare dip in form as of late.

The Briton wasted no time in sweeping aside the Czech, who he had an on-court row with during a match at last year’s Munich Open, as he powered to a 6-3, 6-2, 6-2 success.

Murray will play Spaniard Marcel Granollers in round two.

Australian Bernard Tomic, who opted to play in a tournament in Mexico City rather than represent his country at the recent Olympic Games following a row with Chef de Mission Kitty Chiller, was again involved in controversy as he was beaten by Damir Dzumhur of Bosnia.

Tomic was involved in a public spat with a member of the crowd, with the on-court microphones picking up expletives before he told the spectator: “I will give you some money to make you feel good."

The 23-year-old, who lost 6-4, 6-3, 4-6, 7-6, later apologised for his actions.

Big-serving Croat Ivo Karlovic set a new US Open record as he sent down 61 aces in his 4-6, 7-6, 6-7, 7-6, 7-5 triumph over Taiwan's Lu Yen-Hsun, while Japan’s Kei Nishikori dropped a set on his way to overcoming Benjamin Becker 6-1, 6-1, 3-6, 6-3.

Rio 2016 silver medallist Juan Martin del Potro proved too strong for compatriot Diego Schwartzman, progressing with a 6-4, 6-4, 7-6 victory, with Janko Tipsarević of Serbia ousting Djokovic’s Wimbledon conqueror Sam Querrey of the United States 7-6, 6-7, 6-3, 6-3.