The 21-year-old managed to earn a 7-6(7) 7-6(2) victory in one hour and 48 minutes.
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The 2015 French Open champion failed to create a single break point in the first set, which was forced into a tie-break.
Kyrgios raced to a 3-0 lead in the breaker, but Wawrinka fought back with a double break before drawing level 6-6.
It was the Australian, though, who broke to take the first set, but he struggled to carry that momentum to the second as games went by way of serve.
Another tie-break was needed to separate the two competitors, and once again, Kyrgios came out on top 7-2.