The mercurial Australian, who defeated Rafa Nadal the night before in a match where the Spaniard later criticized Kyrgios' on-court demeanor, was focused in the quarter-final and outplayed Wawrinka in the match's biggest moments despite crowd that vocally backed the Swiss.
The night did not begin well for the hard-hitting Kyrgios, who slipped while hitting a backhand in the match's opening game, opening up a cut on his right hand that required medical attention.
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Leg cramps, which also required a visit from the trainers, followed in the deciding set but nothing could derail Kyrgios, who won his final service game at love to keep his hopes of a maiden championship at the tournament alive.
Next up for Kyrgios is either big-serving American John Isner or his eighth seeded countryman John Millman, who play later on Thursday.
Earlier in the day Briton Cameron Norrie cruised past American Mackenzie McDonald 6-3 6-2 to book his ticket to the semis.
Norrie will face second-seeded German Alexander Zverev, who did not face a break point en route to a 6-4 6-4 win over Australian Alex de Minaur.
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