"This is a special group of guys who've been through a lot," Rodgers said. "It's been a roller coaster."
Back after missing seven games with a broken left collarbone, Rodgers found a wide-open Cobb on fourth-and-8 to wipe out a one-point deficit with 38 seconds left.
The Bears had one final drive, but Jay Cutler's deep pass to Alshon Jeffery was intercepted by Sam Shields on the final play.
That gave the Packers (8-7-1) their third straight division title and fifth postseason appearance in a row. It also kept the Bears (8-8) out of the playoffs for the sixth time in seven years.
Things weren't looking great for the Packers after Chicago's Brandon Marshall spun away from Tramon Williams in the end zone on the first play of the fourth quarter to make it 28-20. But Green Bay answered with a touchdown drive.
Eddie Lacy ran in from the 6 after a 22-yard pass from Rodgers to Andrew Quarless went through safety Chris Conte's hands, making it a one-point game.
Then, on the winning drive, Green Bay converted twice on fourth-and-1 before Rodgers eluded pressure and unleashed that winning pass to Cobb.
A block by John Kuhn on Julius Peppers helped Rodgers roll to the edge and find Cobb by himself down the field.
"We had a blitz on," Bears coach Marc Trestman said. "We lost an edge. Aaron was able to get outside. Once he got outside things happen. When you've got a zero blitz on, things can happen. And we just lost coverage with our eyes in the backfield."
For Rodgers, it was a strong finish after a shaky start, and it gave him some payback against the team that nearly ended his season.
He was intercepted on the Packers' first two possessions but threw for 318 yards and two touchdowns in his first appearance since he was injured in a loss to Chicago on Nov. 4.
Jordy Nelson had 161 yards receiving. James Starks ran for 88 yards. Lacy aggravated his ankle injury in the third quarter and finished with just 66.
For the Bears, their first season under Trestman ended the same way five of the previous six did under Lovie Smith on the outside looking in at the playoffs.