Australia's Wimbledon finalist beat Medvedev 6-7 (2/7), 6-4, 6-2 to produce his second career upset of a reigning number one after ambushing Rafael Nadal at Wimbledon in 2014.
Kyrgios produced his usual on-court antics, complaining about a high bounce, hitting a ball into the stands to draw a warning and bickering with his player box in moments of tension.
But after gathering his formidable resources, the 27-year-old ranked 37th finished off the match in exactly two hours. "This is our fourth meeting and we know each other well," Kyrgios said. "I don't go in looking at the rankings, just the guy in front of me. "I had a clean objective today -- play a lot of serve and volley and execute better. "Hopefully I can keep this rolling and keep on winning.
Medvedev is a machine -- he's number one for a reason." Both players were coming off weekend title wins, Kyrgios at the Washington 500 on Sunday and Medvedev at Los Cabos, Mexico, on Saturday.