Upton, who along with Johnson was dealt from the Diamondbacks to Atlanta in the off-season, went 4-for-5 with a two-run homer, crushing a pitch 440 feet with his brother B.J. Upton aboard in the sixth inning to open a 5-1 Braves lead.
Johnson, meanwhile, went 3-for-4 with a two-run shot and three RBI.
Brian McCann also homered and knocked in three runs for the victors, who snapped a three-game skid.
Mike Minor (5-2) tamed the D-backs on one run over 6 2/3 innings, working around eight hits and a pair of walks while striking out four.
Arizona starter Wade Miley (3-2) was tagged for seven runs (six earned) on six hits over five full innings.
Paul Goldschmidt socked a solo homer for the Diamondbacks.