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.
- 'I'm not listening!' - Kyrgios hits back at Nadal's 'lack of respect' jibe
- Watch Kyrgios attempt underarm serve, frosty handshake with Nadal
- Kyrgios saves three match points to down Nadal in Acapulco
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.
'You don't have to fool yourself' - Nadal accepts Djokovic will win most Grand Slams
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.
'I'm better than you!' - Kyrgios lifts lid on 'uncomfortable' Serena doubles match
Djokovic helps Serbia to win over Austria; Spain and Italy win