Teague also notched seven assists in a 102-100 victory for the visitors as Chicago’s record dipped below .500 for the first time this season, leaving them at 36-37 and further adrift of the Eastern Conference playoff positions.
The Bulls’ season has gone into a nosedive in recent weeks, with the team losing 11 of their last 17 matches to plummet down the standings.
The team held a clear-the-air meeting at the weekend after a damaging defeat to the Orlando Magic on Saturday but were always chasing the game against the Hawks, who opened up a 15-point lead in the second half.
A sustained Chicago rally saw them claw back the scoreline to 93-93 with 1:40 remaining but Atlanta regrouped and regained the lead with free throws from Kent Bazemore, Thabo Sefolosha and Teague.
Jimmy Butler scored a four-point play to take the Bulls back to 98-97 with 19.6 seconds to go, but the Hawks held firm and four more free throws from Kyle Korver and Teague sealed the win.
The win saw Atlanta improve to 45-30, with nine wins in their last 10 games.
Elsewhere Monday, LaMarcus Aldridge scored 31 points and 13 rebounds as an under-strength San Antonio Spurs cruised to a 101-87 win over the Memphis Grizzlies in Tennessee.
San Antonio, who have the second best season record in the league at 62-12, could afford to rest Tony Parker, Tim Duncan and Manu Ginobili.
Kawhi Leonard was also missing with a bruised quadricep. But the Spurs’ effective second string was still way too powerful for the Grizzlies, who lost their third straight game.
In Toronto, Kevin Durant poured in 34 points while Russell Westbrook added an incredible eighth triple-double in his last 15 games as the Oklahoma City Thunder romped to a 119-100 victory over the Raptors.
Westbrook finished with 26 points, 12 assists and 11 rebounds while Durant chipped in with eight rebounds and eight assists.
The win extended the Thunder’s winning streak to a season high of eight games, improving their record to 52-22.
In Florida, Dwyane Wade finished with 30 points and nine assists as the Miami Heat outlasted the Brooklyn Nets 110-99 at the AmericanAirlines Arena.
Seventeen of Wade’s points came in a first half scoring spree, while Hassan Whiteside added 27 points.
“He made a lot of tough baskets,” Nets centre Brook Lopez said of Wade.
“He controlled the game, controlled the tempo. It was vintage D-Wade stuff.”
Wade meanwhile revealed he had narrowly avoided a serious right thumb injury after falling awkwardly in the first half.
“I was diving for a loose ball,” Wade said. “I almost got caught the wrong way, but I’m good.”