The Hawks (20-13) were back in Milwaukee for the first time since winning a pivotal Game 6 in the first round of the playoffs to send the series back to Atlanta where they won to advance.
They were impressive once again, opening a double-digit lead in the first quarter and shooting 50.7 percent from the field for the game.
Marvin Williams and Jamaal Crawford each had 14 points.
John Salmons scored 18 for the Bucks, who struggled in their first home game after a successful Western Conference trip.
Milwaukee (12-17) put together an 8-1 run in the second half to close to 61-53, but Josh Smith, who finished with 13 points, responded with a jumper over Chris Douglas-Roberts that restored Atlanta's double-digit lead.
Salmons, who had 12 points in the third, hit a 3 that cut it to 69-62, but the Bucks' rally fizzled. Williams made a long jumper and Johnson added a fadeaway that made it 77-67 heading into the fourth.
Milwaukee failed to mount a run in the final quarter, and the lackluster play continued. The Bucks shot 37.3 percent from the field and went 4 for 15 from 3-point range.
Smith, not well liked in Milwaukee after his comments about the city during the postseason, didn't even have his name announced correctly at one point, being called "Josh Howard" by the public address announcer.
The Hawks returned all their main players from last year but first-year coach Larry Drew took over for Mike Woodson. Drew has tried to change up the offensive schemes to keep Atlanta from being predictable.
It certainly looked as if Milwaukee had no idea what the Hawks were doing despite coming in as one of the best defenses in the league and winning two of three on a Western Conference trip that included a win over the Lakers.
Smith scored eight points early and Atlanta grabbed a 52-35 lead on Smith's alley-oop dunk from Johnson. Johnson hit a runner in the lane that made it 57-39.
Milwaukee was without several key pieces again.
Brandon Jennings is out at least three more weeks after left foot surgery. Drew Gooden is dealing with his own left foot injury that's caused him to miss three games and nine of the last 14. Carlos Delfino hasn't played since early November with lingering symptoms of a concussion.