Bryant accounted for all of the game's second-half scoring in a contest dominated by the defenses.
Matt Ryan ended the day 26-of-43 passing for 273 yards for Atlanta (3-1), seven of which went to Roddy White for 104 yards.
Falcons running back Michael Turner was largely held in check, compiling 50 yards on 16 carries.
Alex Smith went 21-of-32 through the air for 188 yards and hurled a touchdown pass to Vernon Davis for the 49ers (0-4). But he also threw a pair of interceptions while in Falcons territory, contributing to the setback.