Dennis Schroder added 18 points and 11 assists as the Hawks snapped a three-game losing streak despite committing 21 turnovers.
Jimmy Butler scored 24 points and Andrew Wiggins added 18 to lead the Timberwolves.
Atlanta was sloppy with the basketball all night, but found itself leading 87-84 after rookie Tyler Dorsey knocked down a 3-pointer with 7:26 to go in the fourth quarter.
Dorsey hit another 3-pointer later in the fourth quarter as the game stayed tight into the final minutes.
Minnesota was down 101-100 and had the ball, but was unable to get the ball inbounds and was called for a five-second violation.
Schroder made two free throws on the Hawks' ensuing possession to push the lead to 103-100.
Butler misfired on a contested 3-pointer from the right wing in the final seconds and the Hawks prevailed, with Schroder sinking two more free throws.
Jeff Teague, who spent his first seven seasons in the NBA with the Hawks, had a rough night against his former teammates. He missed his first six shots and finished with just two points on 1-of-9 shooting, though he did have 10 assists. Teague and Taj Gibson also drew technical fouls in the fourth quarter with the game in question.
The Timberwolves led 58-55 after a competitive, up-tempo first half. Butler had 13 points in the first two quarters, and Minnesota scored 17 points off of 10 Atlanta turnovers to take the lead into halftime.
The Hawks were able to make up for the turnovers in the first half to stay close, but more miscues in the third quarter resulted in a Timberwolves run.
Wiggins had a dunk and a layup, and Butler scored off an assist from Towns to push Minnesota's lead to 71-60.
The Hawks answered with a 7-0 spurt capped by a 3-pointer from Bazemore and trailed only 79-76 heading into the fourth quarter.
Minnesota has to make the overnight trip up to Toronto for a matchup with the Raptors on Tuesday.
The Hawks host Charlotte on Wednesday.
--Field Level Media
Minnesota | Atlanta | |
Jimmy Butler 24 | Scoring | Kent Bazemore 22 |
Jeff Teague 10 | Assists | Dennis Schroder 11 |
Karl-Anthony Towns 13 | Rebounds | John Collins 11 |
Jimmy Butler 9 | Free Throws Made | Dennis Schroder 8 |
Taj Gibson 4 | Steals | Malcolm Delaney 2 |
Jimmy Butler 1 | Blocks | Kent Bazemore 2 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Minnesota | 100 | 47.0 | 7-19 | 15-18 | 24 | 35 | 5 | 15 | 14 |
Atlanta | 105 | 49.4 | 13-34 | 14-16 | 27 | 44 | 8 | 8 | 21 |