As Alexei Popyrin, Adam Walton and Tristan Schoolkate all crashed out, de Minaur hit the go button in a straight-sets victory over Japanese qualifier Shintaro Mochizuki.
The world No.8 did not have it all his own way, de Minaur staving off 11 break points in the opening set before seizing control for a 6-2 6-4 6-2 victory on showcourt Stadium 17.
While de Minaur showcased his electric court speed, Kasatkina had to overcome painful cramping and a dogged opponent to also avoid the Australian exodus on day five.
Kasatkina battled back from a service break down in the deciding set to live up to her 15th seeding and deny her friend and former compatriot Kamilla Rakhimova a memorable 24th birthday in a two-hour, 22-minute epic at Flushing Meadows.
Kasatkina expressed pure relief at joining de Minaur and Australian qualifier Priscilla Hon in the last 32 with a fighting 6-2 4-6 7-5 comeback victory.
"When I was 4-1 down, I was just like, 'Oh my God'. I I also started cramping," the world No.18 said.
"I don't know actually how I was able to come back and win.
"My finger was cramping. My quad was cramping. I was just running on the court trying to finish as quickly as possible.
"I'm really happy with my effort today because even though I was not playing my best tennis, I was still able to get this win."
Playing her third grand slam since switching allegiances in March, the Russian-born ring-in looked on track for a cruisy win when leading by a set and a break.
But Kasatkina took her foot off the pedal and world No.65 Rakhimova pounced, reeling off five straight games to level the match and take control of the deciding set.
Showing true grit, though, Kasatkina stormed back to book a third-round tussle with two-time Open champion Naomi Osaka.
While Kasatkina and Hon march on, Popyrin was unable to repeat his 2024 heroics in bowing out in straight sets against top-seeded titleholder Jannik Sinner.
Triumphant over the great Novak Djokovic on Arthur Ashe Stadium last year, Popyrin perished 6-3 6-2 6-2 against Italy's rampant defending champion.
"I was able to put pressure on his serve but, when push came to shove, he came up flush," Popyrin said.
"There's not much you can do when you come up against those players.
"What can I say, he stepped up when he needed to. I guess that's why he's No.1 in the world."
Walton, who had enjoyed the best win of his career when defeating 22nd seed Ugo Humbert in the opening round, succumbed 7-6 (7-5) 6-2 4-6 6-4 to Hong Kong's Coleman Wong.
Schoolkate fell to 23rd seed Alexander Bublik 6-3 6-3 6-3 in less than two hours.
Australian teenager Maya Joint was in action on Thursday night (Friday AEST), taking on 2025 Wimbledon runner-up and eighth seed Amanda Anisimova on Louis Armstrong Stadium.
Hon has a big opportunity to advance to the last 16 on Friday (Saturday AEST) against American world No.58 Ann Li.
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