On a hot, humid day at Flushing Meadows, Edmund was left bathed in sweat while a cool and collected Djokovic stayed on course for his 18th Grand Slam title and improved his 2020 match record to 25-0.
It stands as the second best start to a season since the Serb went 41-0 in 2011.
With the two other members of the sport’s Big Three – Roger Federer and Rafa Nadal – absent from the tournament, Djokovic is heavy favourite to hoist the trophy and the Serb overcame a slow start to show why.
Edmund took a tight opening set, laying down an ace to clinch the tiebreak 7-5.
It was only the sixth set Djokovic had dropped going all the way back to the Australian Open and he did not surrender another to the 44th-ranked Briton.
A serve that was misfiring in the first began to find the mark in the second with the Serb securing the early break on an Edmund double fault on the way to levelling the match.
Djokovic again seized the initiative in the second with back-to-back breaks to jump ahead 4-1 but struggled to close out the set, Edmund rallying to cut the advantage to 5-4 before the three-times champion held for a 2-1 lead.
When Djokovic broke to open the fourth, Edmund’s last bit of resistance vanished and the Serb delivered an emphatic knockout punch to set up a third-round clash with Germany’s Jan-Lennard Struff.
Elsewhere fifth-seeded German Alexander Zverev saw-off 19-year-old American Brandon Nakashima 7-5 6-7 (8) 6-3 6-1 in the second round, while Belgium’s David Goffin ousted South African Lloyd Harris 7-6 (6) 4-6 6-1 6-4 in the second round.