Top seed Djokovic, 28, eased into round three by beating Croatian Borna Coric 6-2 6-4 in an hour and 18 minutes.
The 20-year-old Kyrgios saw off his Swiss rival 7-6 (9-7) 7-6 (6-2).
Last year, he was given a suspended 28-day ban and $25,000 (£17,250) fine after making lewd remarks about Wawrinka's girlfriend during a match.
World number one Djokovic, beaten by 55th-ranked Jiri Vesely last month, won 85% of points on his first serve against the 19-year-old Coric, who is nicknamed 'Mini Djokovic' because of his playing style.
