The Bucks trailed by 11 points heading into the final period but tied the game with 7 minutes to go and dominated down the stretch.
Boykins had 11 of his 20 points in the fourth period and Maggette had 22 overall, while making 8-of-12 shots from the field. Carlos Delfino contributed 15 points for the Bucks, who made 10-of-20 from 3-point range and snapped a two-game skid.
Milwaukee shot 61 percent in the fourth period.
Jamal Crawford scored 20 points for Atlanta and Al Horford contributed 17 points and 10 rebounds. Horford had missed the previous two games with a sore right ankle.