The Australian, who reached the Wimbledon final earlier this summer, produced a superb display of power and touch to win 7-6 (11) 3-6 6-3 6-2. Medvedev defeated Novak Djokovic to win his maiden Grand Slam title in New York 12 months ago but was beaten by the best player under the lights in Arthur Ashe and will now lose the number one ranking. Kyrgios has spoken at length about his team’s influence and desire to make the months away from Australia count by finally living up to his immense talent. “I’ve been in some really tough situations mentally and some really scary places,” the 27-year-old said. “Obviously, if you look at it on paper, they probably didn’t expect me to win it. I might get a set or two if I’m lucky. Give people a show. “It’s a great win. But I come off the pitch and I’m almost relieved it’s over because there’s so much pressure every time I go on the pitch, so much expectation, so much unpredictability of what I can do. “I’m just sitting there in the locker room afterwards and I’m really proud of the performance because it really was a moment where I didn’t think I was capable of producing and doing it anymore. “I just struggled so hard mentally for the first six, seven years of my career. I had great results, shocking results, I tried really hard, then tanked. I honestly didn’t know how to deal with any of that. Beating myself up was unhealthy. “Looking back, it’s just been a learning process until now because I’ve matured so much. I know the process now of what it takes to get to a grand slam final. Not to win it yet, but to win in the final. “It’s the last big tournament of the year. We have to try and keep pushing each other, keep being positive. Next week we go home. But probably three more matches, then you don’t have to play tennis again.” Kyrgios entered the contest fresh from a win over Medvedev in Montreal last month and drew first blood after an epic tiebreak in the opening sets. Leading 4-1, Kyrgios slammed his racket into the court as Medvedev leveled at 5-5, but the Russian could not take any of the three set points. The momentum swung to Kyrgios and, after another swing of his racquet on a missed opportunity, he played an ice-cold drop shot and then clinched his fourth set point. The Australian’s focus faltered in the second set but now he knows how to bounce back and from the start of the third he was locked in, grabbing Medvedev’s serve time and time again and powering one of the best wins of his career. Kyrgios was even able to comfortably fend off an odd moment early in the third set when he appeared to have set up a break point, but reached the net post to deflect a ball from Medvedev’s side, thus forfeiting the point. The Russian later revealed he was not feeling well, blaming the United States’ love of air conditioning, but credited Kyrgios with his performance. “It was a high-level match,” Medvedev said. “I’ve played Novak, Rafa. They all play amazing. Nick today played at their level, in my opinion. If he plays like this until the end of the tournament, he has every chance to win it.” Rafael Nadal is in pole position to take over the world No.1, although Casper Rudd and Carlos Alcaraz are also in contention. Medvedev said: “I’m not going to cry inside [press] room, but I’m a little disappointed. For a few days I will be a little sad, looking at my phone, my laptop or watching some series. “But that’s the motivation, try to do better. Obviously it was the last slam of the year. I didn’t do well enough.” In the last eight, Kyrgios will face another Russian in Karen Khachanov, who defeated Pablo Carreno Busta 4-6 6-3 6-1 4-6 6-3. There was also a five-setter between Matteo Berretini and Alejandro Davidovic Fokina, which the Italian 13th seed won 3-6 7-6 (2) 6-3 4-6 6-2 to set up a clash against Rudd. Don’t forget to follow us at skysports.com/tennis, our Twitter account @skysportstennis & Sky Sports – on the go! Available to download now on – iPhone & iPad and Android