Of the four previous times that Jack Draper and Carlos Alcaraz had stood across the net from each other, half had ended with a distraught Briton aborting the match because of injury. While Draper attempted to keep up with the most successful player of his generation, their rivalry underlined the biggest obstacle in his career: his physical frailty.

Physically, mentally and in every other category, however, the British No 1 has dramatically improved over the past year as he has established himself as one of the very best players in the world. Amid a fortnight that has showcased the best tennis of his life, the 23-year-old held his nerve in a turbulent, chaotic tussle to close out a remarkable 6-1, 0-6, 6-4 win over Alcaraz and reach his first Masters 1000 final at Indian Wells.

“I feel incredible obviously to beat Carlos in this sort of stage in the tournament on that court,” said Draper. “I have watched the top players in the world play on that court for many, many years now, and it feels amazing, honestly, both those things. Obviously I’ve got one more to go tomorrow, so all my sort of feelings and emotions on that, but obviously very proud of myself and the achievement.”

By sealing the most special win of his career, Draper’s arrival among the elite is now undeniable. He is a top 10 player at last and will rise to a new career high ranking of at least No 9 on Monday. He is also the first player in three years to defeat Alcaraz at Indian Wells, breaking his 16-match winning streak. Draper, the 13th seed, will face the 12th seed, Holger Rune, on Sunday as he tries to win his first Masters 1000 title. Earlier, the 21 year-old Dane had defeated Daniil Medvedev, the fifth seed, 7-5, 6-4 to reach his fourth Masters 1000 final.

Draper has tried to pace himself after sustaining a hip injury during the off-season in December and Indian Wells marks just his third tournament of the season. Over the past week, however, he has truly hit his stride, and he had already produced some of the best tennis of his career en route to the semi-final with a run that included a complete dismantling of the No 4, Taylor Fritz.

Alcaraz may have begun the contest as by far the most experienced player on the court, but it was the Spaniard who looked nervous and uncertain early on. The 21-year-old lost his opening service game with two double faults, which set the tone for a dire opening set as he littered the court with groundstroke errors and responded to every mistake simply by trying to hit the ball harder.

While Alcaraz struggled, Draper refused to offer him a way back into the set. He served well early on, soaked up his opponent’s first strike with his excellent defence and, most of all, he maintained his composure. After 23 minutes, the Briton had closed out the set with ease.

Carlos Alcaraz plays a hefty forehand. Photograph: Mark J Terrill/AP

Predictably, Alcaraz’s woes did not last. He quickly began to find his range early in set two. After two bruising deuce games, the Spaniard emerged with the break. Suddenly, he was landing ample returns, dominating with his forehand from inside the baseline and serving well in decisive moments. As he scrambled to react to Alcaraz’s rapidly rising level, Draper lost authority and confidence in his own game. He ended the set moving gingerly and barely winning points.

After conceding such a one-sided second set against one of the best players of the 21st century, many players would have fallen away. Following a brief bathroom break, Draper dug deep early in set three and forced himself to re-establish the energy and intensity he displayed early in the match. He began to serve and move well again while injecting pace into his forehand once more. After he held serve at the beginning of the set, an early turning point came following a slapstick passage of play at 1-1, 15-15 on Alcaraz’s serve, as the match featured the first double video review in the history of professional tennis.

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Draper had chased down Alcaraz’s drop shot when the umpire, Mohamed Lahyani, ruled that the ball had bounced twice. Draper immediately requested a video review, which showed that the ball had clearly not bounced twice. After Lahyani ruled that the point should be replayed, Draper then requested a second video review to determine whether the umpire’s call had hindered Alcaraz, whose subsequent shot had landed out. The second video review, along with the point, was ultimately awarded to Draper. Two points later, Draper led by a break.

Having earned the biggest opportunity of his career, Draper refused to let the moment pass him by. He served excellently throughout the final set and, as his defence soaked up the Spaniard’s first strike, unforced errors began to leak from Alcaraz’s game again. After snatching a second break in the set, Draper was broken back once but showed his mental fortitude by closing out the biggest win of his career at the second opportunity, moving him closer to the dreams he has spent his life chasing.

“It was my goal at the end of last year that I obviously had some good results, but I want to really achieve some consistency and get to the point where I’m pushing these top players in the world in the biggest tournaments,” said Draper. “That’s the goal of mine. So to come through the match today, that means so much to me, especially against a player of Carlos’s calibre.”