The 19-year-old was playing his first match since reaching the quarter-finals of the Australian Open after suffering a back injury.
He capitalised on two of his three break points for the 68-minute victory over the American.
“I’m just glad to be back. It was killing me not being able to play, especially after the Australian Open,” Kyrgios told the official ATP Tour website.
“I was loving it. I had a good time back home, and I was ready to get back out there and start competing again. I thought I played really well for my first match back.”
Kyrgios now faces world No 11 Grigor Dimitrov in what will be their first career meeting.
“He’s one of the best players in the world right now and that’s why I play the sport, to have a chance to go out there and compete against the best players in the world,” he said. “I’m just going to go out there and have a lot of fun again.”
In other men’s first-round action, Sergiy Stakhovsky rallied for a 2-6 6-4 6-2 victory over Sam Querrey to set up a second-round meeting with ninth seed Tomas Berdych.
Jack Sock also overcame a first-set deficit, the American battling back for a 6-7 (4-7) 6-2 7-5 victory over Yen-Hsun Lu.
Diego Schwartzman overcame Jerzy Janowicz 6-4 3-6 7-6 (7-3). The Argentinian will play second seed Roger Federer next.
Slovakian Martin Klizan got past Pablo Andujar 7-6 (7-4) 6-3, while American Steve Johnson saw off Marcel Granollers 6-2 6-3 and Victor Hanescu defeated Mikhail Youzhny 6-3 6-4.
Andrey Golubev, Alexandr Dolgopolov, Donald Young, Michael Berrer, Igor Sijsling, Denis Istomin, Simone Bolelli, Robin Haase and Malek Jaziri all also reached round two.