After navigating the most important two weeks of his blossoming career with formidable ruthlessness and self-belief, Jack Draper walked on to Arthur Ashe Stadium for the biggest match of his career fully aware that the challenge required him to elevate both his game and physicality to new levels in order to contend with the No 1 men’s player, Jannik Sinner.

Despite fighting with everything he had, Draper was unable to show his best qualities as he struggled physically in humid conditions, vomiting multiple times. In one of the most turbulent matches of the tournament, Sinner, who himself suffered a wrist injury, edged out the British No 1 7-5, 7-6(3), 6-2 in a three-hour, three-minute psychodrama to reach the US Open final for the first time. He will play the USA’s Taylor Fritz, who beat his compatriot Frances Tiafoe over five sets in Friday’s other semi-final.

Related: Jack Draper shows in defeat he has the game to match world’s best | Simon Cambers

With his 54th win of this immense breakout season, Sinner is the first Italian man in history to reach the US Open singles final. Having won 34 of his 36 matches on hard courts this year, the Australian Open ­champion will look to cap off his ­season by winning his second grand slam ­tournament of the year.

The past few weeks have been a remarkable period in Sinner’s career. A week before the US Open began, the 23-year-old announced he had twice tested positive for the banned substance clostebol in April before an independent tribunal determined last month that Sinner bore no fault or negligence for the presence of the banned substance in his body due to contamination.

Both players moved through their opening service games with authority and early in the match, as they were evenly matched from the baseline in the various long, physical exchanges, the difference between them was Draper’s serve. In a tough deuce game at 5-5, he struck three ­double faults, including one on break point, to hand over the decisive break of the set.

Early in the second set, the match descended into chaos as it became clear that Draper was struggling. He was sweating profusely, ­sent multiple rackets off-court for grip changes and then changed his soaking shoes because they had become too “dangerous” for him to compete in. From midway through the second set, Draper vomited multiple times on to the court and his mobility gradually decreased. Even though he was struggling, Draper still managed to find big serves and excellent shotmaking to keep hold of his serve and eventually force a tie-break.

“The second set I was feeling not too great, and I still pushed it to a tie-break,” said Draper. “I was fighting hard. I’m proud of myself. I tried to fight as hard as I can. Just not going to get it done against someone like that.”

At 4-4, 40-15 on Draper’s serve, Sinner produced one of the best points of the tournament, a brilliant defensive effort ending with him deflecting a big smash from Draper with a massive forehand winner in response. But Sinner had slipped during the point and his wrist was hurt. He took a medical timeout after Draper held serve as the Briton was also treated by the doctor. Sinner said: “The physio loosened it up very fast on court, so after I felt OK in the beginning. Then after it went away by playing, which is good. Let’s see how it is tomorrow when it’s cold.”

Related: Fritz outlasts Tiafoe over five sets in all-American clash to reach US Open final

As both players struggled physically, Draper looking sickly as ­Sinner avoided hitting backhands. But the Italian regrouped and closed out the second set in a ­dominant tiebreak. With ­Sinner leading by two sets and Draper ­looking practically out on his feet, the third set was merely a formality as the world No 1 closed out the match to reach his second career grand slam final.

Although Sinner is just four months Draper’s senior, the pair began the match with a wide gulf in ­experience. Almost every aspect of this semi-final run has been new territory for Draper, who had reached only one grand slam fourth round beforehand, whereas Sinner has spent the last three years inside the top 20 and he is already just the fourth active player to reach the semi-finals of all four grand slam tournaments. Draper believes that his physical problems stemmed from his inexperience.

“I think obviously it’s a big occasion for me,” said Draper. “Even though I generally feel pretty relaxed and stuff, I definitely felt more excited today, a few more nerves around. I’m definitely someone who is, I think, quite an anxious human being. I think when you add all that together sometimes I do feel a bit nausea on court, and I do feel a little bit sick when it gets tough.”

Draper believes that some of the physical problems he has suffered over the past few years are due to the anxiety he sometimes feels before matches, which stems from his determination.

“I think I’ve got quite a strong mentality and I use up a lot of mental energy a lot of the time because I want it so badly,” he said. “But obviously that doesn’t necessarily help a lot of the times, especially in these five-set matches and that sort of anxiety and those feelings can build up. So it’s definitely just something that is a real strength of mine but also a weakness, and I have to continue to work on it.”

Draper’s physical problems have defined his career so far. He has worked extremely hard and made significant strides to reach the point where he is robust enough to perform on the ATP Tour week after week, and to piece together this superb breakthrough run in New York. But as he departed the stadium, he left with the knowledge that there is more work to be done.

“I think I just need to keep on learning, keep on growing, keep on having situations like today where I came unstuck and, how am I going to do it different next time and all these types of things,” Draper said. “That’s the biggest thing. I think it is, honestly, just a matter of time. It’s experiences, doing all the right things, it’s training consistently, and over time you just progress and you get stronger and you get better.”