The 78th-ranked Bulgarian, who had dropped all seven prior meetings with Federer, made a dramatic fightback to defeat the Swiss third seed 3-6, 6-4, 3-6, 6-4, 6-2 at Arthur Ashe Stadium and will face Russian fifth seed Medvedev in Friday's semis.
There was an extended break between the fourth and fifth set as Federer took a medical timeout and left the court.
"In a fourth round like this, if you can keep it nice, short, simple - you have to take them", Federer said. "I fought with what I had".
Federer appeared to regain some momentum in the third set, taking advantage of Dimitrov's double-fault on a break point at 3-3 and winning the next three games. Talking about his slow start to the tournament, Navratilova said that the reason for it was more emotional than technical. "For sure, in the end, he was not 100 per cent of himself".
Coming into the U.S. Open, the 78th ranked Dimitrov, dubbed "Baby Fed" because of the similarities between his game and Federer's, did not look much of a threat, posting just one win from his last eight matches.
Opponents of no-deal Brexit defeat British PM Boris Johnson in parliament
Johnson's government will now seek to hold a vote on Wednesday to approve an early election, most likely to be held on October 14. Mr Johnson spoke today after suffering a major defeat in Parliament when rebels seized control of the Brexit agenda.
Bank employees stage protest against Centre's decision to merge PSU banks
Union Bank, Andhra Bank and Corporation Bank will be consolidated, and Indian Bank and Allahabad Bank will coalesce. However, despite these moves, the country's largest lender, the State Bank of India, may emerge as a big victor .
Indonesia deports 4 Aussies for demonstrating in Papua
Massive mobilizations have entered their second week in West Papua with the police letting loose repression on the protesters. Jakarta took control of the former Dutch colony in the 1960s after an independence referendum widely viewed as a sham.
"I feel really odd but I am happy to be in my first major semi".
He joins Novak Djokovic on the sideline less than two months after their epic five-set Wimbledon final.
Federer is 6-0 against Dimitrov on hard courts and, should he move on, would bring unbeaten records on the surface into a semifinal against either Wawrinka (17-0) or Medvedev (3-0). Those allowed Dimitrov to race into a 4-0 lead he was never in danger of surrendering, one of the most unexpected results of recent history sealed when Federer went wide. He also was trying to add to his totals of five U.S. Open championships and 20 major trophies in all.
Instead, Dimitrov advanced to his third major semi-final, and his first in NY.