Green Bay will host San Francisco next weekend in the wild-card round.
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 the Packers 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 unleashed that winning pass to Cobb.
It was a strong finish after a shaky start for the superstar quarterback, and it gave him some payback against the team that nearly ended his season.
Rodgers was intercepted on the Packers' first two possessions, with Conte picking him off in the end zone on the first one. He also threw for 318 yards and two touchdowns in his first appearance since Nov. 4. He got knocked out of that game on an early sack by Shea McClellin at Lambeau Field, sending the Packers into a 2-5-1 slide.
Jordy Nelson had 161 yards receiving, and Cobb, in his first appearance since Oct. 13, won it with his catch. James Starks ran for 88 yards. Eddie Lacy, hobbled by a knee injury, finished with just 66.
For the Bears, their first season under Marc Trestman ended the same way five of the previous six did under Lovie Smith on the outside looking in at the playoffs.
They had a chance to wrap up the division last week, only to get pounded 54-11 at Philadelphia. And with another opportunity, they came up short against their longtime rivals.
This one is sure to spark memories of Green Bay's victory in the 2010 NFC title game at Soldier Field on the way to the Super Bowl championship and fuel more questions about Cutler's ability to win big games.
With a playoff spot on the line and his contract set to expire, Cutler threw for 226 yards with two touchdowns and an interception. He is now 1-9 against Green Bay, including that conference final and a loss with Denver in 2007.
Matt Forte ran for 110 yards and two scores. He also had 47 yards receiving with a touchdown catch.
Alshon Jeffery had 80 yards receiving, and Brandon Marshall had 74.
Two unusual plays late in the first half turned a 7-3 deficit into a 13-7 advantage for the Packers.
Green Bay had a first down at the Chicago 17 when a sack and strip against Rodgers by Julius Peppers turned into one unusual touchdown. Jarrett Boykin ran across the field, picked up the loose ball as play stopped. One thing, though: The whistle never blew.
With Rodgers standing nearby, Boykin turned and headed 15 yards to the end zone. Rodgers then threw his hands up to signal a touchdown, and after a replay review, it stood.
That stunned the crowd and gave the Packers a 10-7 lead.
Green Bay caught another big break on the Bears' next possession when Jeffery fumbled a pass at the Chicago 41. Morgan Burnett picked up the ball and lateraled to Sam Shields, who returned it to the Chicago 28. That led to a 27-yard field goal by Mason Crosby to make it a six-point game at the half.