After a dour first half saw neither team able to click offensively, Khris Middleton sparked a game-changing third-quarter run for the Bucks.
Stepping up in the absence of Giannis Antetokounmpo who sat with a knee injury, Middleton scored 16-straight points out of the half-time break to bring Milwaukee to the brink of their first finals appearance since 1974.
However, the Hawks were determined not to let the Bucks cruise to the finish line.
Cam Reddish led a late rally for Atlanta which reduced a 22-point deficit to just six in the closing minutes.
But his 21-point effort was ultimately not enough as the Bucks held on to clinch the series four games to two.
Middleton top-scored for Milwaukee with 32 points, while Atlanta’s Trae Young was still hobbled by the ankle injury he suffered earlier in the series, only managing 14 points.
Game one of the best-of-seven NBA Finals series gets underway on Tuesday night (Wednesday UK time).