The downtown dagger came in the fourth quarter Wednesday night at Vivint Smart Home Arena in Salt Lake City, Utah.
The Jazz and the Eastern Conference's second-place squad were tied at 94-94 with about six seconds remaining when the play developed.
Celtics point guard Shane Larkin dribbled the ball just past half court, before driving to his right past Ricky Rubio. He drew three Jazz defenders in the paint, before throwing a pass back out to Semi Ojeleye at the 3-point line.
Ojeleye did a quick ball fake, before passing off to Brown on his right. Brown threw up a 3-pointer with no hesitation. He sank the shot, giving the Celtics a late 3-point advantage.
Jazz guard Donovan Mitchell came up empty on the game's final attempt, giving the Celtics their 52nd victory of the season.
"[I was] super confident," Brown said after the game, according to the team website. "As soon as it left my hands, I was like 'man, this has got to be good. If any one is good, this one is.'"
"I'm just happy it went in because I had nothing left for overtime."
Brown scored a team-high 21 points and had five rebounds, three assists and two steals in the win. Mitchell netted a game-high 22 points for the Jazz.
The Celtics host the Eastern Conference-leading Toronto Raptors at 7:30 p.m. Saturday at TD Garden in Boston.