The Australian, who entered the tournament as a wildcard, demolished the current world number 7 in straight sets.
Rublev was in good form ahead of the contest, but fell to a 6-3 6-0 defeat against an opponent who is currently ranked outside the world's top 100.
Speaking after the match, Kyrgios underlined the importance of being at peace, saying: "Obviously I'm extremely happy. Obviously always happy when you play like that, but I know that things can change very quickly. It's just another win for me or another loss. I just take it as it comes.
"I feel like I'm at that point in my life where I'm at peace with everything off the court, and I guess I'm just in the right mindset.
"Look, it's just one match. I'm not going to say like anything crazy, because, you know, I played my first round, I was very lucky to get through. Played a hell of an opponent.
"Today I played great and he may not have played his best. I'm definitely happy, yeah, but I'm just focusing on doubles tomorrow."
Elsewhere, second seed Alexander Zverev was taken to a final set decider against 166th ranked Borna Coric. Despite this, he ultimately came out on top, winning 6-4 3-6 6-3 to reach the third round in a gruelling match.
Germany's number one said: "I felt like, 'OK, if I'm going to lose, I'm going to go for it'. It worked out."
Reilly Opelka was forced to retire from his match against Argentina's Francisco Cerundolo after sustaining a shoulder injury.
Hugo Gaston, in contrast, knocked out American John Isner following a 7-6 6-4 win.
Isner, who won this event in 2018, produced 22 aces and only had his serve broken once. However, he went for 0 for 5 when it came to his own break opportunities.
Jannik Sinner, who is the current world number nine, held off the challenge of Emil Ruusuvuori as he enjoyed a 6-4 3-6 7-6 win.
Casper Ruud, Fabio Fognini, Alexander Bublik, Pablo Carreno Busta and Gael Monfils also booked their place in the next round, while Diego Schwartzman endured a disappointing loss at the hands of Thanasi Kokkinakis.