Last year the 20-year-old got a suspended 28-day ban and $25,000 fine after making lurid remarks about Swiss Wawrinka's girlfriend during their match at the Rogers Cup in Montreal.
Kyrgios, who has had several brushes with authority, was widely criticised, but his 7-6(7) 7-6(2) second round victory on Wednesday was further proof of a growing maturity after he won his first ATP title earlier this year in Marseille.
There was the odd outburst at the umpire, one after a first serve during the first-set tiebreak was called out despite appearing to clip the line, but Kyrgios kept his emotions in check to edge a tight tussle.
Japan's Kei Nishikori, the sixth seed, had a narrow escape before joining Kyrgios in the third round.
Italy's Fabio Fognini recovered from losing the opening set to level the match and served for the match at 5-4 in the decider before imploding.
Nishikori won 6-2 3-6 7-5 to set up a meeting with Frenchman Richard Gasquet.
World number one Novak Djokovic was back to his ruthless best as he thumped Croatian tyro Borna Coric 6-2 6-4.
Djokovic suffered his earliest defeat for three years when Czech Jiri Vesely beat him on his 2016 claycourt debut at last month's Monte Carlo Masters but if Coric harboured any hopes of pulling off another upset, Djokovic snuffed them out by breaking the 19-year-old three times.
(Reporting by Martyn Herman; editing by Ken Ferris/Toby Davis)
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