He returned from a broken collarbone and is taking aim at a postseason run, even if it took one big pass to get there.
"This is a special group of guys who've been through a lot," Rodgers said. "It's been a rollercoaster."
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.
Green Bay will host San Francisco next weekend in the wild-card round.
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.
Then, on the winning drive, Green Bay converted twice on fourth-and-1 before Rodgers eluded pressure and unleashed that winning pass to Cobb.
"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.
Cobb, in his first appearance since Oct. 13, caught just two passes but both were for touchdowns.
"To be in that moment at the end of the game and have that opportunity, it's a blessing," Cobb said.
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.
This loss 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 even though he played well.
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.
Marshall guaranteed Cutler will be back next season, and Cutler said he'd like to return.
"You'd love to," Cutler said. "You can't predict the future, though. I'm not really going to get into what's going to happen. It always works out how it's supposed to."
Matt Forte ran for 110 yards and two scores. He also had 47 yards receiving with a touchdown catch.
Jeffery had 80 yards receiving, and 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 Peppers turned into a wild 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, 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 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.
As for Boykin's fumble recovery, Rodgers said it was one of the strangest plays he could recall.
"Boykin finally picked it up, I looked back at (referee) Clete (Blakeman), he was looking at us so I think myself and everybody on the sideline was telling him to start running," Rodgers said. "It was one of the crazier plays I've been part of."
Bears RT Jordan Mills had his left foot in a walking boot and was on crutches after being injured on the game's first offensive series. ... Green Bay's Josh Boyd suffered a hip injury in the second half.
Lance Easley, the referee who made the infamous "Fail Mary" call in 2012, plans to contact back judge Gregory Wilson about Monday's controversial call to offer support.
Several Buffalo Bills players accused star receiver Odell Beckham Jr. of throwing punches after plays late in the New York Giants' 24-10 win in Buffalo.
The NFL has asked the Browns why Pro Bowl cornerback Joe Haden was inactive for Sunday's game vs. San Diego after being listed as probable on the injury report.
An Indianapolis Colts source has denied multiple reports that star quarterback Andrew Luck has a partial shoulder subluxation, according to ESPN's Mike Wells.
The Vikings traded Gerald Hodges, who started the first four games of the season, to the 49ers in exchange for a sixth-round pick and center Nick Easton on Tuesday.
A group of anonymous Lions fans bought space on seven billboards around the Detroit metro area to protest the non-call after a Seattle player batted the ball out of the end zone Monday.