Australian Open champion Sinner made the last eight for the second time by seeing off US 14th seed Tommy Paul 7-6 (7/3), 7-6 (7/5), 6-1.
Medvedev, the 2021 champion and runner-up to Djokovic last year, outclassed Portugal's Nuno Borges 6-0, 6-1, 6-3 to reach the quarterfinals for the fifth time in six years.
Women's world No 1 Iga Swiatek, meanwhile, stayed on course for a sixth Grand Slam title with a straight-sets win over Russia's Liudmila Samsonova.
The Italian Sinner recovered from 4-1 down in the first set to see off Paul, who had been hoping to join compatriots Taylor Fritz and Frances Tiafoe in the quarterfinals in New York.
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