World No 1 Djokovic had to overcome a bit of an early scare as he dropped the first set against Edmund but came back strongly to win the second round encounter with the scoreline reading 6-7 (5/7), 6-3, 6-4, 6-2.
The Serbian ace extended his winning streak in 2020 to 25 matches and looks in sublime form to win a 4th US Open title at Flushing Meadows.
"I'm really glad having an early kind of tough match because it kind of serves me better I think for the rest of the tournament," said Djokovic.
The 17-time Grand Slam champion is looking to close the gap on his arch rivals Roger Federer and Rafael Nadal, both of whom are not competing at the US Open, in the race for the all-time men's Slam singles title record.
The 33-year-old Serbian who won a record eighth Australian Open title earlier in February is on 17 grand slam singles titles, with Nadal on 19 and Federer on 20.
Pliskova who was billed as the top seed in the women's singles draw was sent packing out of the tournament after being stunned by World No. 50 Carolina Garcia in straight sets 1-6, 6-7. While Garcia completely dominated the opening set against Pliskova winning it 6-1, the top seed Czech fought hard in the second set but it was too late for her to stage any kind of comeback into the match.
Pliskova said her defeat was nothing to do with being elevated to the top of the draw after a host of high-ranking withdrawals over coronavirus fears."No, zero pressure from this for me. This is nothing to do with my loss today," she sniffed.
In the other major results in the men's draw on Wednesday, fifth seed Alexander Zverev defeated American wildcard Brandon Nakashima a hard fought four set encounter, winning the match 7-5, 6-7 (8/10), 6-3, 6-1.