Bell broke a 31-31 tie with a 1-yard scoring run with 1:25 left in the game after safety Troy Polamalu forced a fumble by Packers quarterback Matt Flynn at the Packers' 17-yard line.
Green Bay had one last chance to score following Micah Hyde's 70-yard return on the ensuing kickoff but Flynn's pass on the game's final play went off Jarrett Boykin's fingertips in the end zone at snowy Lambeau Field.
Ben Roethlisberger passed for 167 yards with two touchdowns and an interception and ran for a score as the Steelers (7-8) kept their faint post-season hopes alive with their fifth win in seven games.
Bell finished with 124 rushing yards and Cortez Allen scored on a 40-yard interception return for Pittsburgh.
The Packers (7-7-1) also remained in the playoff hunt despite the loss but needed a loss by Chicago later Sunday to avoid elimination.
Flynn, making his seventh straight start in place of the injured Aaron Rodgers, completed 21-of-39 passes for 232 yards with a touchdown pass to Boykin.
Swim Week Miami Beach 2014 [PHOTOS]