Blaine Gabbert made his first start of the season for the 49ers, replacing the struggling Colin Kaepernick as the team's starting quarterback, but he was unable to find the endzone on his first drive.
There was no early touchdown for the visitors either, but the Falcons did get some points on the board as Matt Bryant kicked a 44-yard field goal.
Quinton Patton hauled in a 41-yard pass from Gabbert as the San Francisco offense came back onto the field, before the quarterback came up just short while trying to run it in himself, but a short pass for Celek on the next play gave the home side the opening touchdown.
Phil Dawson restored the 49ers' four-point advantage with a field goals, before Shaun Draughn and Pierre Thomas ran the ball for the home side, setting up Gabbert to find Celek in the endzone again just before the break.
Atlanta did manage to cut the lead in the final seconds of the second quarter though as Jones hauled in a 54-yard catch, setting up Freeman for a sprint across the line.