Johnson finished with 24 points, connecting on 10 of his 18 shots from the field, while Deron Williams provided 19 points and nine assists as Brooklyn notched a third straight win.
Brook Lopez helped the Nets snap a 13-game drought against the Bucks with 19 points and nine rebounds.
Milwaukee, meanwhile, fell for the fifth time in six contests despite 34 points from Brandon Jennings.
Ersan Ilyasova (21 points, nine rebounds) and Larry Sanders (14, eight, six blocks) also turned in good performances in the Bucks' tough loss.
Notable deaths of 2014 [PHOTOS]