World number five Tsitsipas was fined $10,000 for unsportsmanlike behavior – the highest single fine at the tournament so far.
After the match, he apologized for hitting a ball in the stands, which is considered a separate offense in the Grand Slam rulebook.
Kyrgios, who won the match in four sets and faces American Brandon Nakashima in the fourth round on Monday, was fined $4,000 for an audible indecent offense.
That means the Australian has been fined $14,000 so far at this tournament, after he was punished for spitting in the direction of a spectator he said he was respecting during his first-round match against Britain’s Paul Gibb.
After Saturday’s heated competition, Tsitsipas and Kyrgios continued to exchange criticism off the court – the Greek fourth seed called his opponent a “villain” and a “bully”, while Kyrgios said Tsitsipas was “unlikeable” in the locker room.
“I did nothing to Stefanos today that is disrespectful,” he added. “I wasn’t digging him with balls. Coming here and saying I terrified him, that’s anything but soft.”
The 27-year-old has reached the quarter-finals of the Grand Slam on two previous occasions – a record he could equal with a win over Nakashima when the pair meet on Center Court.