Blake, who retained his Sydney International title last week, used terrific court coverage and pinpoint accuracy to see off the 19-year-old world number 216 on Rod Laver Arena in an hour and 21 minutes.
Kuznetsov threatened a tougher match when he broke Blake's opening two service games, but the 27-year-old's experience shone through as he dismissed his Ukrainian-born opponent and regular practice partner.
With a title under his belt this season, the Blake finally believes he is worthy of a long-term place in the world's top 10.
"I've continued to work hard, so I'm not surprised by the fact I continue to get better," said Blake, who crushed former world number one Carlos Moya in his opening-round match.
"It's just a matter of competing consistently on the tour, and being at the top of my game. It seems like that in finals, in big matches, in semis, and now it's a matter of taking it to a grand slam."
Blake, beaten by Roger Federer in last year's showpiece Masters Cup final in Shanghai, has never gone beyond the fourth round at Melbourne Park, and now feels he has the game to be a genuine contender on the biggest stages of all.
"Hopefully, I can have some success here, but if not I'll know I'll have confidence going into the French Open and Wimbledon and the U.S. Open, that I can be there in the second week. I just hope it starts here."
He next meets either Robby Ginepri of the U.S or German qualifier Mischa Zverev.