The hot-headed Australian lost his cool and expressed his frustrations at umpire Carlos Bernardes during a close opening set.
The 26-year-old complained about court speed and had several heated arguments with the official - even calling the Brazilian an "absolute clown".
As the match headed into a tie-break, Kyrgios was docked a point for smashing his racket before producing a double fault and losing the opening set.
Jannik Sinner turned on the style in the second and completed the 7-6 6-3 win in one hour and 40 minutes.
During that second set, Kyrgios was docked an entire game for smashing another racket. He also posed for a selfie with a young fan who ran onto the court.
Speaking during his on-court interview, Sinner said: "Today I raised a little bit my level. I had to, because he's a very aggressive player, especially when he serves well. I'm very happy about my performance today.
"I think when I saved a couple of break points early in the first set, it raised my confidence a little bit. Then it was not easy on this one side where the sun was completely in the eye, which you have to manage a little bit the situation also."
Sinner, who is currently 11th in the ATP rankings, could deny Cameron Norrie a place in the top 10 after the Brit endured a disappointing straight sets defeat to Norway's Casper Ruud.
Playing with heavy strapping on his left leg, the British number one struggled to put on his best showing against the Norwegian.
Norrie needs Sinner, Taylor Fritz and Hubert Hurkacz all to bow out of the Miami Open before he can call himself a top 10 player in the world.
Elsewhere, Daniil Medvedev moved within one victory of regaining his world number one status.
The Russian progressed to the quarter-final courtesy of a 7-5 6-1 victory over Jenson Brooksby. He now has to beat Poland's Hubert Hurkacz in order to move ahead of Novak Djokovic in the ATP rankings.