Tomic beat the 97th-ranked Brown 7-6 (7-2), 6-4, 7-6 (7-3) to book his fourth-straight appearance in the second round of the final major of the season.
The Australian, ranked 67 in the world, will face fourth seed David Ferrer in the last 64 after the Spaniard progressed with a 6-1, 6-2, 2-6, 6-2 triumph over Damir Dzumhur.
Tomic’s compatriot Marinko Matosevic departed the tournament, however, losing 6-3, 6-4, 7-6 (7-4) to five-time champion and second seed Roger Federer.
Five-time champion Roger Federer advanced to the second round of the US Open on Tuesday with a 6-3, 6-4, 7-6 (7-4) victory over Australian Marinko Matosevic.
Federer was cruising against the 76th-ranked Matosevic with a two-set lead and a break in the third before his opponent broke back to eventually force the tie-breaker.
“It was a bit more difficult than I thought it was going to be,” admitted Federer, who is seeking an 18th major singles title but his first since Wimbledon 2012.
He will face another Australian, 104th-ranked Sam Groth for a third-round berth.
Groth advanced to the second round with an encouraging straight-sets win over Spaniard Albert Ramos.
The big serving Groth triumphed 6-3, 7-6 (7-5), 6-3.
Federer’s first-round match was a special moment for the 33-year-old, who finally got the chance to meet his childhood hero, NBA great Michael Jordan.
“He (Jordan) was just my hero of all sports,” Federer said.
“That’s what he was for me growing up.
“Besides (Stefan) Edberg and (Boris) Becker being my tennis idols, I had Jordan as my all sports idol.
“I just remember when I was younger; in Germany it was really big on the German TV stations.
“That’s where I saw him doing all his moves. I wasn’t necessarily a Chicago Bulls fan or anything like that.
“It’s just I was into him, into the incredible athlete, just being that guy who was carrying basketball at the time.
“So I guess that’s what inspired me.”
Federer’s opening match was more methodical than inspirational but Jordan appeared genuinely interested in what was unfolding on centre court.
Even though they had just met it was clear that Federer and Jordan share a unique bond, their excellence uniting them in a way few could understand.
“His longevity, the way he made it look easy, his will to win, wanting to be the best, delivering under pressure, being a superstar in a team sport, carrying his team for so many years,” said Federer, rolling out a long list of superlatives that many would use to describe his career.
“There’s so many things that he did well and represented the game really nicely, I thought.
“That’s why he also became my idol.
“He wanted to know some things about tennis. How I prepare, all these things, how much I play, where I go next.
“These kind of things, you exchange each other’s ideas about your respective sports and that’s kind of what you talk about.”