Kyrgios described Tomic as the most hated athlete in Australia when the pair exchanged barbs over who was the better player on Instagram on Wednesday night.
Medvedev remained calm as a robot in the face of fanatic support for Kyrgios to secure a clinical 7-6(1) 6-4 4-6 6-2 win.
The tennis maverick, Kyrgios, returned to the combustible John Cain Arena and gave raucous fans a night to remember.
On Thursday, the pair engaged in a spat on social media that clearly escalated.
Before a men's doubles match with partner Thanasi Kokkinakis, the Australian imitated the way Djokovic celebrates victories with extravagant gestures to all four corners of the stadium.
The ATP announced on Wednesday that the season will resume on August 14 with the Washington Open.
Novak Djokovic, Ash Barty and Simona Halep have all indicated they would have concerns about playing the tournament under the health protocols designed to keep them safe.
Australian Kyrgios was a match for the 19-time Grand Slam champion in the second and for most of the third set but the muscle-bound Spaniard always looked like the most likely winner once he got his nose back in front.
The 24-year-old Australian raged at the umpire, raged at himself and raged at his box but ultimately prevailed in the longest match of his career.
Nadal, a 6-3, 7-6 (7/4), 6-1 winner over Argentina's Federico Delbonis, miscued a shot that hit a ballgirl in the head, but he melted hearts when he apologised and gave her a kiss on the cheek.