Forward Carlos Boozer continued his impressive start to the season with 32 points and 11 rebounds for the Jazz while Matt Harping made a lay up with 1.8 seconds as the Jazz clung on after earlier blowing a 24 point lead.
Redd's 57 points broke the Bucks' single-game record of 55 set by Kareem Abdul-Jabbar against the Boston Celtics on December 10, 1971.
The 2004 All-Star scored the NBA’s highest individual score of the season with 18-of-32 from the field, 6-of-12 from 3-point range and 15-of-17 free throws.
Utah led by 24 points late in the second quarter before Redd willed Milwaukee all the way back, tying the game at 111-111 on an off-balance 3-pointer with Deron Williams in face with six seconds remaining in the game.
On Utah's next possession, Harpring slipped inside the lane for the game-winner.
Everyone knew Redd would get the last shot, and he did, but his 26-footer near the top of the circle failed to find the target, making the Jazz 5-0 when they score 100-plus points.
Williams had 27 points and dished out 15 assists and Harpring added 17 points for the Jazz, who shot 54 percent and have won six of their first seven games.
In Cleveland, LeBron James scored 22 of his 38 points in the last 17 minutes on Saturday as Cleveland erased a big third-quarter deficit to beat Boston 94-93.
While in Atlanta, Seattle guard Ray Allen' winning lay-up denied Atlanta their longest National Basketball Association winning streak in eight years.
Allen finished with 33 points as the SuperSonics posted a 113-112 triumph over the red-hot Hawks on Saturday.