Murray had beaten 37th-ranked Kyrgios in straight sets in their three previous meetings, eliminating him this year from two other grand slams, in the Australian quarter-finals and third round of the French Open.
The third-seeded Scotsman sent Kyrgios packing in the first round after playing straight man to the flippant Australian, who unnecessarily tried ‘tweener’ shots through his legs and jumped extravagantly on routine forehands that he buried into the net.
“I expected a very tough match, and that’s what I got,” Murray, 28, said.
But Murray had the last laugh against the clownish Kyrgios as he blasted 18 aces and 46 winners while only committing 23 unforced errors under the lights at Arthur Ashe Stadium.
Earlier, second seed Federer was the envy of a clutch of men’s players made to work overtime in the 90-degree heat by quickly dismissing his opening opponent.
Federer, who has been in sizzling form since reaching the Wimbledon finals, dashed past 34th-ranked Leonardo Mayer of Argentina 6-1 6-2 6-2 to launch his campaign for a sixth U.S. Open crown and first slam title since the 2012 Wimbledon.
“I feel good now,” said Federer. “I actually wasn’t so confident yesterday and today. I just felt like maybe (this)could be one of those matches I just couldn’t see coming.
“Thankfully I took this match extremely serious,” said the 34-year-old Swiss, who had fought off five match points in beating Mayer last year in Shanghai.
Murray next meets French left-hander Adrian Mannarino, while Federer faces Belgian Steve Darcis, who advanced 6-7(2) 6-3 6-2 3-1 when Marcos Baghdatis of Cyprus retired.
Baghdatis became the fifth player to retire on Tuesday after seven quit their matches on Monday as the toll of late season injuries and the searing heat presented severe challenges at the U.S. National Tennis Center.
Among other shortened matches, Australian Lleyton Hewitt, the 2001 U.S. Open winner, advanced 6-0 7-6(2) 1-0 when Aleksandr Nedovyseov of Kazakhstan retired.
Misfortune favoured the French and went the other way for the Aussies when 12th seed Richard Gasquet advanced 4-6 6-1 4-6 6-3 2-0 when Thanasi Kokkinakis retired.
Other players were sorely tested on the court.
Three players in the bottom half of the men’s draw had to go the distance under the sun, including French 11th seed Gilles Simon, who looked to have iced victory after taking a 6-2 6-4 3-0 lead over American Donald Young.
But the Frenchman stumbled, and the 26-year-old American, once hailed as the next great U.S. player, saw an opportunity and turned the match upside down for a 2-6 4-6 6-4 6-4 6-4 win.
“I really had it on my racquet,” said Simon. “I was not able to do anything on the tennis court. I think Donald realised it and then played what he had to play to take me down in five sets. It’s a terrible result for me today.”
In another wrenching defeat for France, Paul-Henri Mathieu fell to Japan’s Yoshihito Nishioka in five sets.
The 128th-ranked Yoshihito Nishioka, who saw fourth-seeded compatriot and 2014 finalist Kei Nishikori drummed out in five sets on Monday, booked himself into the second round with a 6-4 2-6 6-7(7) 6-1 6-2 victory.
Dutchman Robin Haase also made a Houdini-like escape against Germany’s Dustin Brown to register a 4-6 4-6 6-3 7-5 6-4 victory.
On the women’s side, second seed Simona Halep of Romania also had an abbreviated match as she advanced 6-2 3-0 after 47 minutes on court as New Zealand’s Marina Erakovic retired with a knee injury.
Also sprinting to victory was fourth seed Caroline Wozniacki, who dismissed U.S. national college champion Jamie Loeb 6-2 6-0, and fifth-seeded, two-times Wimbledon winner Petra Kvitova beat Germany’s Laura Siegemund 6-1 6-1.
The women’s draw continued to produce upsets as Czech sixth seed and French Open finalist Lucie Safarova fell 6-4 6-1 to Ukrainian Lesia Tsurenko.
Fourteenth seed Timea Bacsinszky of Switzerland was also shown the door, sent out by 42nd-ranked Czech Barbora Strycova 7-5 6-0.
“I wasn’t surprised (by the upsets), it is normal,” said 23-year-old Halep. “Everyone is fighting like crazy because it’s the last grand slam (of the year).”
(Editing by Frank Pingue/Sudipto Ganguly)