Top-seeded Federer was unable to conjure up any of his old magic after the Czech made a flying start and stormed to a surprise 7-6 6-4 3-6 6-3 victory.
"It couldn't be better," Berdych said in a courtside interview. "There is no better feeling. There is no better moment than this one."
Federer was unable to hide his disappointment.
The 31-year-old had ended a two and a half year Grand Slam drought by winning Wimbledon in July and arrived in New York on the back of a victory at the Cincinnati Masters.
"I had such an amazing summer. I really thought I was going to come out and play a solid match," he said. "I didn't do that tonight. Obviously there is a bit of a letdown now."
While Berdych has never won a Grand Slam, the gifted sixth seed has been a thorn in Federer's side before, most famously in 2010 when he beat the Swiss master at Wimbledon.
Berdych made a nervous start in the bear pit that is the Arthur Ashe Stadium, losing his opening service game, but was almost untouchable for the next 90 minutes, cracking winners to every part of the court.
Federer was staring at defeat when he went down a break in the third set but through sheer force of will, he raised his game and won the set, unsettling Berdych with perfectly disguised drop shots and some outrageous passes down the line and across the court.
"I still was down two sets to one, so I wasn't celebrating too much," Federer said.
"The momentum switch no doubt gave me a chance, put the score back to zero, put him further away from winning, and made the match go longer, make it more physical, more mental.
"Obviously I was excited winning the third, but the problem was the first couple of sets, particularly the first one."
Berdych regained his composure in the fourth and claimed the crucial break in the eighth game before serving out for victory.
"There is something in my game that he doesn't like and it makes him struggle a bit, I would say, and maybe bring him out of his comfort zone that he always like to be on court," Berdych said.
"He always likes to have a time and he always like to be the one dictating the game."
Berdych's semi-final opponent is Britain's Andy Murray, who won the Olympic gold medal in London, and lurking on the other side of the draw is the defending champion Novak Djokovic.
For Federer, a five-times winner at the US Open, it marked the first time he had failed to make the last four since 2003, the same year he won the first of his record 17 Grand Slams titles.
"Obviously I wish I could have played better," Federer said.
"There were so many moments I thought, man, it's just not happening for me. It was just a very disappointing match for me."