Guard Andrew Wiggins scored 33 points, including eight down the stretch, and the Timberwolves won 117-107 despite letting a 34-point lead temporarily slip away.
"Those last minutes, Andrew was unbelievable," Minnesota interim coach Sam Mitchell said. "We tried to get the ball in his hands, and he was feeling it. ... He was amazing."
The Hawks (7-2) took a 107-106 lead on a basket by forward Paul Millsap, but Wiggins converted a three-point play with three minutes left, and the Timberwolves (4-2) pulled back away from there.
The Timberwolves had lost 12 straight in Atlanta since recording a 103-93 victory on Nov. 20, 2002.
Forward Kevin Garnett, in his 21st season, played in that game, but more than a few of his present Minnesota teammates were in elementary school at the time. It looked as if the Timberwolves' inexperience might prove costly.
Minnesota led 81-47 before the Hawks closed the third quarter on a 37-12 run behind 14 points by guard Jeff Teague to pull within 93-84 going into the fourth. Atlanta then kept up the comeback.
"We got frazzled," Mitchell said.
Wiggins, though, pulled the Timberwolves through as they improved to 4-0 on the road.
The reigning NBA Rookie of the Year sank 15 of 22 shots and got support from rookie center Karl-Anthony Towns, who finished with 17 points, 12 rebounds and three blocked shots.
"We stayed confident," Towns said. "We just had to weather the storm."
Wiggins scored 31 points in an overtime victory at Chicago on Saturday, and he wouldn't be denied with the game on the line again.
"He was a superstar who wanted to end the game on his terms," Towns said when asked about Wiggins. "That's what I saw."
"He made plays after we were able to get up a point," Hawks coach Mike Budenholzer said. "He did a little bit of everything."
The Hawks, who scored 19 points off 10 Minnesota turnovers in the third-quarter rally, shot 72 percent in the third, with Teague going 6-for-8 and Millsap making all four of his shots.
"They were shooting the ball so well that I knew it was going to be tough to come all the way back," Teague said. "But we made it a dogfight."
Teague finished with 24 points and a game-high nine assists. Millsap added 22 points.
For the game, Minnesota shot 57.5 percent and Atlanta hit 51.2 percent from the floor. The Wolves compiled a 40-27 rebounding advantage.
The Timberwolves shot 63.8 percent and beat the Hawks 22-11 on the boards while building a 72-42 halftime lead.
"They came out playing very aggressively, and we came out without a lot of energy," said Hawks guard Kyle Korver, who was held to five points. "We're a team that has to play with a lot of energy, and we finally responded in the second half."
Asked what the difference was, Korver had a simple answer.
"You just get mad once you're embarrassed," he said.
Wiggins made eight of 10 shots for 16 first-half points. Minnesota guard Zach LaVine had 13 points at the break, and guard Kevin Martin had 11, missing only three shots between them.
The Hawks opened the game 1-for-9 and the Timberwolves were up 30-19 through the first quarter thanks to shooting 59.1 percent and forcing seven turnovers.
Minnesota finished with 19 turnovers that led to 35 Atlanta points. Thanks to Wiggins, though, the Timberwolves held on for the streak-breaking victory.
"Our guys were resilient and just kept playing hard," Mitchell said. "It would have been easy (to fold) once Atlanta made the big push."
NOTES: G Kevin Martin, averaging a team-best 18.8 points off the bench, was back with the Timberwolves after missing Saturday's win in Chicago and three practices while attending to a family matter. ... G Tim Hardaway Jr. was on the Hawks' inactive list, and he hasn't played this season despite being healthy. He was acquired from the New York Knicks for a first-round draft choice after averaging 11.5 points last season. ... The Timberwolves, who began a stretch of four games in five days, host the Charlotte Hornets on Tuesday to end their first back-to-back set. ... Minnesota has lost both of its home games. ... The Hawks play the New Orleans Pelicans on Wednesday in their third consecutive home game. ... Minnesota C Nikola Pekovic, who had Achilles surgery in April, has begun light running, but he remains out indefinitely. ... Timberwolves G Titus Jones, a first-round draft pick out of Duke, was again inactive.