The British number one is continuing to live up to his top-10 ranking and kept 19-year-old Rune at arm’s length during a 7-5 6-4 6-1 victory at Flushing Meadows to reach the fourth round for the first time.
Rune, already the highest-ranked Danish man in history and a French Open quarter-finalist this year, has a reputation as a spiky character and during the second set he protested to the umpire about Norrie catching his ball toss before serving.
Players are allowed 25 seconds between points but the clock stops when the server throws up the ball, meaning catching the toss buys extra time to reset.
Rune implied to the umpire he thought Norrie was deliberately exploiting a loophole in the rules, although he was more diplomatic in the press room later.
“I think it’s a fine balance,” said the teenager. “You have those 25 seconds and the umpire accepts that if you’re at one second and you do it you can let it go and take five, 10 seconds to bounce it again and then serve, and then you all of a sudden have 10 seconds.
“It’s a bit annoying. I’m not controlling the rules but I think you can do it a couple of times but doing it 10, 15 times is maybe too much.”
Responding, Norrie said: “I’m not doing it on purpose. I’d love to go out there and have a perfect ball toss every time and get up there and hit rockets. It can happen sometimes. I’d rather play quick. I like to play quick.”
Norrie, whose run to the Wimbledon semi-finals was the first time he had gone beyond the third round at a slam, opened up a 5-3 lead in the first set but hit a wild double fault and then shanked a smash to drop serve, only for Rune to play a similarly poor game and give him a second chance.
The British number one looked to have taken control of the second set at 4-1 but Rune was able to apply some late pressure again after feeling dizzy and consulting the doctor, forcing Norrie to save two break points at 5-4.
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The pair had met twice before, with both matches going to a deciding set, but here Rune could offer no real resistance in the third as Norrie eased to victory.
The seventh seed, who admitted he battled through nerves in his second-round win over Joao Sousa, said: “I thought I played a bit better than I did in the previous match, so that was great. I felt way more comfortable. It was nice to be on Grandstand.
“It was tough playing against Holger. He can come out and play very aggressive and can come forward very well. He’s extremely talented, and he’s a young up-and-coming player, but it was nice to get through in straight.
“I think it’s great with the seeding. You can work your way more into the tournament than going out there, having to play a top seed early on. I’ve still got a lot of things I would like to improve, and I’ve got tomorrow to do that.”