Kyrgios, seeded 28th, fired 24 aces to four for Johnson and made eight double faults, twice Johnson's total.
"I knew I had to play top-flight tennis," Kyrgios said. "I had to serve well. I'm happy to get through."
Kyrgios won ATP titles earlier this year at Acapulco and Washington.
The Aussie will next face French wildcard Antoine Hoang as he tries to take full advantage of a draw quarter that opened greatly with upsets Tuesday.
Ousted were Austrian fourth seed Dominic Thiem, Greek eighth seed Stefanos Tsitsipas, Spanish 10th seed Roberto Bautista Agut, Canadian 18th seed Felix Auger-Aliassime and British 30th seed Kyle Edmund.
The only higher-seeded players than Kyrgios who made the second round in his draw quarter are 13th-seeded Frenchman Gael Monfils and Italian 24th seed Matteo Berrettini.
Kyrgios has never gone past the third round at the US Open. His best Grand Slam results have been quarter-final runs at the 2015 Australian Open and Wimbledon in 2014.
While the conclusion came at 1:12 a.m., it wasn't the latest-finishing US Open men's first-round affair. That distinction still belongs to the 1991 Jimmy Connors defeat of Patrick McEnroe in five sets that ended at 1:35 in the morning.