Kyrgios defeated three top-10 players on the way to the title, saving three match points in a second-round victory over second-ranked Rafael Nadal -- owner of 17 Grand Slam titles -- and beating No. 9 John Isner in the semis.
He also beat three-time Grand Slam winner Stan Wawrinka in the quarter-finals of a drama-filled week that saw him shake off hostile crowds, illness, injuries and moments of malaise -- not to mention a post-match rebuke from Nadal.
His win over Zverev was a remarkably straightforward as Kyrgios frustrated the baseline-hugging German with well-disguised drop shots.
He broke Zverev at love in the fourth game of the opening set and held for a 4-1 lead, prompting Zverev to smash his racquet in frustration.
Kyrgios broke again to open the second set, but double-faulted on break point in the next game.
He broke Zverev again in the fifth game and held with confidence the rest of the way to capture his first title since Brisbane in January of 2018.
In women's action China's Wang Yafan rallied from a set and a break down to capture her first WTA title, defeating American Sofia Kenin 2-6, 6-3, 7-5.
World number 65 Wang, playing in her first WTA singles final, outlasted the 35th-ranked American to claim her breakthrough title after two hours and 10 minutes.
The 24-year-old from Nanjing seized a 2-1 lead in the final set by taking advantage of her third break-point chance in the game.
Wang held on her first ace of the match for a 3-1 lead, but surrendered a break on her fourth double fault to allow Kenin to equalize at 3-3.
After Wang held at love to 5-5, she reeled off the last four points of the 11th game to break Kenin and then held serve for the triumph.
The 20-year-old American was denied her second career WTA title and second crown of the year after taking her first at Hobart in January.