The Hawks made a fourth-quarter charge after trailing by as many as 25 points and got as close as one point, 124-123, with 1:32 remaining.
The Cavaliers (42-18) avenged an early season loss against the Hawks (34-27), their only win in the past 13 games dating back to the 2015 playoffs.
Tim Hardaway Jr. led the Hawks with a career-high 36 points.
Irving led the Cavaliers with a game-high 43 points. James added 38 points, 13 rebounds and eight assists. The game was the return of Kyle Korver, who was traded to the Cavaliers in January. He finished with nine points.