Fifth seed Alexander Zverev recovered from a sluggish start to beat Borna Coric in four sets – and then took a swipe at Martina Navratilova.
Zverev cut an often dejected figure as he lost the first set 6-1 and trailed 4-2 in the second, before finding a way to haul himself through to the semi-finals 1-6 7-6 (5) 7-6 (1) 6-3.
Speaking on Amazon Prime, 18-time grand slam winner Navratilova said the German will not be able to beat the top players playing "pat-a-cake" tennis.
But Zverev hit back: "Maybe she should look at my record against the big guys.
"Maybe she should look that I'm positive against Roger (Federer). Maybe she should look that I've beaten Novak (Djokovic) on multiple occasions in big matches and finals.
"I'm in the semi-finals, and sometimes not playing your best and finding a way is more important than playing your best.
"But she's a grand slam champion, as well, a multiple grand slam champion, she's respected, but her opinion right now does not matter to me."
Coric had punished some pitiful Zverev serving in the opening set but was guilty of a succession of glaring misses in the second set tie-break which ultimately helped set the 23-year-old on the way to victory.
Zverev's win makes him the first German player to reach the semi-finals of the men's singles at the US Open since Boris Becker, who reached the last four in 1995 where he was beaten by Andre Agassi.
Zverev added: "It's great to be in the semi-finals and unfortunately we haven't been there in 25 years for a German player, but there will be many more after me and hopefully I can continue the way I'm going."
Zverev will meet Pablo Carreno Busta, who overcame 12th seed Denis Shapovalov in five sets.
Spaniard Carreno Busta, who was Djokovic's opponent in the previous round when the world number one was defaulted, won a four-hour marathon 3-6 7-6 (5) 7-6 (4) 0-6 6-3.
The 20th seed, who made the last four three years ago, said: "I am destroyed, but I am very happy. After this fight it's tough to say but it's incredible to be in the semi-final again.
"When I play in the US I feel very comfortable. The last few months in quarantine were tough for everyone but I worked very hard with my coach."