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The win sends Medvedev through to his fourth straight final and stretches his win streak to 12 matches.
Coming into the US 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.
The 33-year-old has had a relatively stress-free time at the tournament so far, dropping just one set and getting a walkover in the second round.
The only drama came early when Goffin, seeded 15th, broke Federer to take a 2-1 lead in the first set but the Swiss broke back in the next game and cruised to the finish line.
Djokovic, champion in four of the past five Slams and 16 overall, was less bothered by left shoulder pain that nagged him in the second round in defeating 111th-ranked American Denis Kudla 6-3, 6-4, 6-2.
Bidding for an 18th Grand Slam title, second seed Nadal booked his 11th quarterfinal at Melbourne Park and will meet unseeded American sensation Frances Tiafoe.
German Zverev needed to be at his sharpest to get past the South African stalwart but won the final five points of the third set tie-break to ensure Europe would keep the trophy they won at the inaugural event in Prague last year.
The Greek teenager, who turns 20 on Sunday, followed up his defeat of seventh seed Dominic Thiem, beating four-time champion Djokovic, seeded ninth, in a first-time meeting.
Marin Cilic, the 2017 runner-up, suffered a shock 3-6, 1-6, 6-4, 7-6(3), 7-5 defeat by Argentine Guido Pella.
The win followed the victory for Wawrinka's girlfriend Donna Vekic, who demolished fourth seed Sloane Stephens, earlier in the day.