Maholm (2-0) yielded only a third-inning single to Placido Polanco over seven innings on his way to the victory, which extended his scoreless streak starting the season to 12 2/3 innings.
The left-hander worked around three walks and struck out seven.
Upton cracked a 400-foot-plus solo homer in the sixth inning -- his sixth of the young season -- and scored both Atlanta runs in the win.
Marlins stater Kevin Slowey (0-2) pitched well in the loss, surrendering a pair of runs on six hits over seven innings.
Miami fell for the sixth time in seven games to begin the season.