Despite his slow start, the maverick Australian emerged victorious in typical crowd-pleasing style, showing off with aggressive aces and some exaggeratedly effortless points.
Kyrgios, who was knocked out in the last eight at the US Open, said that despite Majchrzak breaking his serve, there was "never really doubt in my mind that I was going to win".
"I've barely been broken all year," so when "the opponent doesn't really do much to break me it's quite frustrating," he said after the one hour and 21 minute match.
"I was just not playing the right way - the court's very fast," Kyrgios added.
But by being "a bit more aggressive" in the second and third sets, the world number 20 said he "ended up just weathering the storm and then coming through".
"I've got really good confidence in my game right now. So I don't really doubt myself, even when I'm down a set... firing Grand Slams has given me that confidence."
Kyrgios, whose lawyer appeared for him at a court hearing in Australia this week for a charge of common assault, will face either third-seeded US player Taylor Fritz in the quarter-finals.
Fritz beat Japanese player Hiroki Moriya 6-1, 3-6, 6-4, with the crowd rooting for their home favourite right until the end of the nearly two-hour match.
