Blaine Gabbert started at quarterback for the 49ers for the first time this season, after Colin Kaepernick was benched for his struggles so far this season, but the former first-round Draft pick could not open the scoring in the opening drive of the game.
Matt Bryant kicked a field goal for the visitors, but the 49ers took the lead at the start of the second quarter after Quinton Patton hauled in a long throw, setting Gabbert up for a pass to Garrett Celek.
After both sides added a further field goal a piece, Shaun Draughn and Pierre Thomas were running the ball for the home side, before Celek got open in the endzone again, hauling in his second touchdown of the game.
Atlanta made the scores close again just before the break, as Matt Ryan connected with Julio Jones for a 54-yard gain, before completing a short pass to Devonta Freeman, leaving the running back to sprint over in the final seconds of the second quarter.
Gabbert tried to build on his solid first-half performance, completing a long pass down the sideline to Torrey Smith early in the third quarter, but the Falcons forced the first turnover of the game a couple of plays later when Phillip Adams intercepted the ball.
The 49ers briefly had to make a change at quarterback when Gabbert was hit in the head by Philip Wheeler, but Kaepernick featured for just two plays before the former Jacksonville Jaguars passer was able to return, having suffered no ill effects.
Ryan looked down field for his receivers at the start of the fourth quarter, knowing that a touchdown would be enough to hand Atlanta the lead, but the quarterback was sacked by Navarro Bowman, forcing the visitors to punt.
The Falcons soon got another chance as a Gabbert pass was tipped into the hands of Vic Beasley for the second interception of the game, but Jones and Jacob Tamme both missed chances to get the touchdown, forcing the NFC South side to settle for the field goal, leaving them a point down.
The home side got the ball back inside the final couple of minutes, with a couple of runs from Kendall Gaskins ensuring that the Niners ran the clock down enough to hold on for the win.
Despite the win, the 49ers remain bottom in the NFC West, while the Falcons sit second in their division, two wins behind the Carolina Panthers.