Kyrgios brushed off concerns of a hip injury, defeating the German, 6-3, 7-6, 6-3, hitting 20 aces in the one hour and 51 minute win.
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The 22-year-old will play either Malek Jaziri or Kevin Anderson in the second round.
Meanwhile, fellow Aussie men, Thanasi Kokkinakis and Jordan Thompson were both beaten in their first round matches.
Kokkinakis went down 4-6, 6-1, 6-4, 6-4 to Kei Nishikori, while Thompson was defeated by John Isner, 6-3, 4-6, 7-6, 6-3.