The world number 84 faces 2015 champion and top seed Djokovic on Sunday.
Djokovic reached the last 16 when a second successive opponent pulled out through injury at Flushing Meadows.
Edmund joined fellow Briton Johanna Konta in reaching the fourth round while compatriots Andy Murray and Dan Evans will on Saturday seek to join them in the last 16.
Edmund was beaten by Isner in straight sets at the French Open this year but his confidence has risen since he led Britain to Davis Cup victory, without Murray, over Serbia in July.
Isner, 31, fired down 27 aces but could only convert one of his seven break points as Edmund’s serve held up under the pressure.
“It’s been a great tournament so far,” said Edmund, who knocked out world number 15 Richard Gasquet in the first round.
Two-time US Open champion Rafael Nadal of Spain beat Russia’s Andrey Kuznetsov 6-1 6-4 6-2 in the final men’s match of the day.
Nadal, seeded fourth, has not dropped a set in reaching the last 16 of a tournament he won in 2010 and 2013.
“I had a fantastic first set, a little trouble with my serve in the second but the third was key so I’m very happy,” said Nadal.
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