Harriet Dart knocked out of US Open by Ukraine’s Marta Kostyuk

The British number three had chances to take the first set off the 19th seed but could not keep her level up in a 7-6 (10) 6-1 defeat.

Harriet Dart is out of the US Open (Matt Rourke/AP) (AP)

Harriet Dart will have nightmares about the first-set tiebreak in her defeat against Marta Kostyuk as she went out in the second round of the US Open.

Britain’s Dart, who had already served for the opener twice, squandered five set points against the Ukrainian 19th seed, three of them on her serve.

Kostyuk had already missed three of her own in a marathon tie-break but took her fourth opportunity to lead the match.

There was an air of inevitability about the second set as Kostyuk ran away with it to seal a 7-6 (10) 6-1 victory in a match which saw the temperature hit 38 degrees Celsius.

Defeat means Dart could not reach the third round of a second successive grand slam following her run at Wimbledon in July, but she is set for a new career high ranking, provisionally in the high 60s.

It also means her teacher mum, who has been her stand-in coach in New York, will not have a scheduling dilemma as she is due to return on Friday to prepare for next week’s new term.

Her chance to win this match was in that first set, where she was the better player and had more than enough opportunities to win it.

Harriet Dart was beaten in straight sets (Matt Rourke/AP) (AP)

But her first serve went missing and was twice unable to serve it out before a tie-break that neither player will remember fondly.

Fifteen of the 22 points went against serve, with three of Darts coming when she had set point.

The second set was a precession for the Ukrainian, who coasted to it with three breaks of serve.