Coco Gauff has cruised to victory to get her US Open title defence underway in New York [Source: AP]

Coco Gauff has had an easy start to her US Open title defence, rolling to a 6-2 6-0 victory over Varvara Gracheva of France.

Gauff needed just over an hour, looking more like the player who won her first major title last year than the one who had dropped her last two matches before coming to New York.

She suffered early exits at tune-up tournaments in Cincinnati and Toronto and there were early signs of trouble as she had five double faults in the first set.

The 20-year-old had to fend off three break points to hold her serve in the second game but the world No.3 found her footing from there, breaking her opponent’s serve in the third and seventh games.

Gauff ploughed through the second set in 27 minutes, upping her level across the board as she produced only five unforced errors and finished with 10 aces for the match on Arthur Ashe Stadium.

“I was just trying to enjoy the match,” said Gauff, who set up a meeting with German Tatjana Maria in the next round.

“I think today was the best tennis I’ve played in a while.

“It was definitely a lot of pressure, this tournament, but I’m just enjoying it … Whatever happens, happens.”

Zheng Qinwen, the women’s Olympic gold medallist, stayed in the tournament by rallying for a 4-6 6-4 6-2 victory over Amanda Anisimova.

Zheng began the grand slam season by reaching the final of the Australian Open. She had a difficult assignment to start the year’s final major in Anisimova, an American who earlier this month reached the final of a hard-court warm-up tournament in Montreal and returned to the top 50 of the WTA rankings.

But the No.7 seed solved Anisimova’s power as the match went on to move into the second round as she turns her attention back to the slams after becoming China’s first singles gold medallist at the Paris Games.

“… To come to the next tournament, I say, everything starts at zero,” Zheng said.

“You are not anymore the Olympic champion. Just be humble and try to work, fight every single match, because if you don’t fight, you have a big chance to lose.”

Maria Sakkari, the No.9 seed from Greece, became the first seeded player to be eliminated when she stopped playing after losing the first set against China’s Yafan Wang. Sakkari, who also lost in the first round last year, received treatment on her shoulder in the first set.

Elsewhere, their were opening wins for Americans Maddison Keys, the 14th seed, Taylor Townsend and Peyton Stearns.