Al Horford led six Atlanta players in double figures with 19 points as the Hawks beat the Cavaliers for the third time in four meetings this season.
It was the final regular-season clash between the two teams considered by many to be the best in the East.
With the win the Hawks are the only team in the league to beat Cleveland three times in this campaign.
But even though it could have been a preview of the Eastern Conference finals, Atlanta's Kyle Korver insisted the Hawks weren't trying to send a message.
"There is no statement win," Korver said. "It's a good win. We'll learn from it, as we keep saying about every game.
"There is no statement win in the regular season."
Paul Millsap and Jeff Teague scored 16 points apiece. Millsap also chipped in eight rebounds and Horford grabbed nine to go with six assists.
The Hawks reserves were also solid. Dennis Schroder scored 15 points with eight assists and Mike Scott contributed 14 points in 17 minutes.
Atlanta forced 18 turnovers, including nine from LeBron James, who shot just 5-of-13 from the floor in scoring 18 points.
Kyrie Irving led the Cavaliers with 20 points, while Kevin Love added 14 with eight rebounds.
The playoff-bound Hawks led by 17 in the first quarter. The Cavaliers trailed by as many as 12 early in the third, before taking their first lead in the period.
The Hawks, however, dominated the first five minutes of the fourth quarter to pull away.
After Schroder's driving layup with 30.2 seconds to go in the third snapped a 79-79 tie, Atlanta began the fourth on a 17-4 scoring run that put the game out of Cleveland's reach.
Korver drained a pair of three-pointers in the run, and Schroder connected from long range before Scott capped the surge with a jump shot that made it 98-83 with 6:50 to play.
Cleveland never got closer than nine points the rest of the way, connecting on just 5-of-17 from the floor in the fourth.
The Hawks outscored the Cavaliers by a 54-24 margin in the paint as Cleveland endured their fifth straight loss in Atlanta.