Edmund, 24, beat Kyrgios - who won the Washington title on Sunday - 6-3 6-4 and will play Russian eighth seed Daniil Medvedev in the next round.

In the doubles, Andy Murray and Spain's Feliciano Lopez beat Lukasz Kubot and Marcelo Melo 6-7 (5-7) 6-3 11-9.

Elsewhere, Dan Evans will play Rafael Nadal in the second round.

It will be the first meeting between Evans and Spain's 18-time Grand Slam champion at tour level after the Briton beat Australian Alex de Minaur 6-4 7-6 (8-6).

Nadal, who is the top seed and defending champion at the ATP 1,000 event, received a first-round bye in his first tournament since losing to Roger Federer in the Wimbledon semi-finals in July.

Edmund keeps his cool to ease past Kyrgios

Edmund never faced a break point against Kyrgios in a rain-affected match, staying calm as the world number 27 argued with the chair umpire for much of the first set about the towels provided courtside.

Kyrgios wanted a white towel as opposed to tournament-branded ones, and after being handed a code violation for an obscenity, was delivered a white towel 20 minutes later.

He was broken midway through the first set, before world number 33 Edmund served out the opener to love.

In the second set, Kyrgios twice saved break point before Edmund finally broke his serve to love to go 5-4 up, going on to seal the win on his second match point with his 15th ace.

Elsewhere, British number two Cameron Norrie was beaten in straight sets by German third seed Alexander Zverev.

Zverev, who won the title in Montreal two years ago, won 7-6 (7-4) 6-4 to set up a third-round clash with Georgia's 13th seed Nikoloz Basilashvili.

Murray and Lopez continue unbeaten run

Murray and Lopez, who won the Queen's title on their debut outing in June, continued their unbeaten streak as a partnership against Kubot and Melo - Murray's partner at Eastbourne.

The wildcards took Kubot and Melo's opening service game before being broken themselves later in the first set, with both pairs saving three set points as the Polish-Brazilian partnership won on a tie-break.

Murray and Lopez came out flying in the second set, going a break up to open a 3-0 lead before the remainder of the set stayed on serve.

In the champions tie-break, Lopez saved match point at 9-8 with an ace before he and Murray won the next three points to clinch victory.

"In the match tie-break, it felt like we were hitting so many good shots and not getting rewarded for it," said Murray.

"It was tight at the end, but we did well to get through."

They will play French Open finalists Jeremy Chardy and Fabrice Martin in the next round.

Elsewhere, Britain's Joe Salisbury and his American partner Rajeev Ram won 7-5 7-5 against the all-British pairing of Jamie Murray and Neal Skupski.