The Falcons had the first possession in overtime and failed to score and Michael Koenen's poor 36-yard punt from the 14-yard-line put the Steelers in a prime spot to notch a win.
On Pittsburgh's first play from scrimmage, Mendenhall found a hole, got a block from tight end David Johnson scampered into the end zone for the victory.
The Steelers' running back finished with 120 yards on 22 carries. Hines Ward hauled down six passes for 108 yards from quarterback Dennis Dixon, who was making only his second career NFL start in place of the suspended Ben Roethlisberger.
Pittsburgh (1-0) extended its streak of wins in opening-season games to a league-best eight.
Matt Ryan led Atlanta (0-1) with 27-of-44 passing for 252 yards, but he tossed a fourth-quarter interception.