The Australian, who has recovered from the hip problem which forced him to retire in the first round at Wimbledon, survived three break points in the opening game before going on to close out the first set with two breaks against the Belgian world number 13.
Kyrgios, who is 23rd in the current rankings and 22/1 for the US Open with Sky Bet, secured another crucial break to lead 5-3 in the second set before wrapping up victory in one hour and six minutes in the testing hot conditions.
Alexandr Dolgopolov of Ukraine booked his second-round match against Kyrgios after the Ukrainian qualifier beat Kevin Anderson of South Africa 6-4 7-6 (8/6).
Sky Bet make Kyrgios their 8/13 favourite, with his unorthodox opponent a 5/4 chance.
Number 11 seed Pablo Carreno Busta of Spain beat Italian Paolo Lorenzi 6-3 6-3.
Twelfth seed Roberto Bautista Agut is out though, after the Spaniard lost 7-6 (7/5) 6-3 to American wildcard Jared Donaldson, while 13th seed Jack Sock lost 7-5 6-4 to Japanese player Yuichi Sugita.
Also through to round two is Juan Martin Del Potro, the veteran Argentine seeing off Czech 10th seed Tomas Berdych 3-6 7-6 (7/1) 6-0, and Russian Karen Khachanov after his 6-1 1-6 6-3 win against Diego Schwartzman of Argentina.
Albert Ramos-Vinolas of Spain battled past Russian qualifier Mikhail Youzhny 6-2 3-6 6-3, while compatriot David Ferrer came through 6-1 5-7 6-3 against David Johnson of the United States.
Georgian Nikoloz Basilashvili beat Borna Coric of Croatia 6-3 7-6 (7-5), Frenchman Adrian Mannarino came from behind to defeat Holland's Robin Haase 2-6 7-6 (10/8) 6-2 which sets up a second-round match against Wimbledon semi-finalist Sam Querrey.
In the evening session, Mischa Zverev beat Fernando Verdasco in straight sets, while Ramkumar Ramanathan came from behind to beat qualifier Christopher Eubanks.
Number eight seed Jo-Wilfried Tsonga was beaten 6-4 7-6 (11/9) by Ivo Karlovic, while 14th seed John Isner saw off wildcard Tommy Paul 6-3 6-3.
