The 38-year-old Serbian tennis player won with a score of 6-4, 6-7 4, 6-2, 6-3. This was his 192nd Grand Slam win on hard courts, surpassing Roger Federer's record, and also his 395th career win at Grand Slams.
Djokovic started smoothly with a cross in the first set, but had to seek medical help for lower back pain. In set 2, he missed the opportunity to break the serve and then lost in the tie-break when he made a double serve at the decisive point. However, experience and courage helped Djokovic quickly regain control of the game, winning 2 consecutive sets to close the match.
The victory over Norrie also increased the head-to-head record between the two players to 7-0 in Djokovic's favor. This is his 16th appearance in the US Open quarter-finals, and he has become the oldest player to reach the round since Jimmy Connors in 1991.
Speaking after the match, Djokovic said he saw the challenge from the opponent as an opportunity to regain the tempo after a period of absence from Wimbledon. In the next round, the second seed will meet Jan-Lennard Struff, the German tennis player who surprised everyone when he eliminated Holger Rune and Frances Tiafoe.
With this victory, Djokovic continues his journey towards the 25th Grand Slam title in his career, a milestone that no other tennis player in history has achieved.
