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Bears kicker Robbie Gould booted a 38-yard field goal to seal the victory, just as he did in Chicago's win against the New Orleans Saints last week.
The bone-chilling -16.6 degrees Celsius game-time temperature was the coldest since the Bears started keeping records in 1963.
Chicago can become NFC North Division champion for the third time in four years if they beat the Texans in Houston and the Minnesota Vikings lose at home to the New York Giants on Sunday.
The Bears' listless play left them with a 14-3 halftime deficit, and two second-half interceptions thrown by quarterback Kyle Orton did nothing to turn the tide.
"When we play in December it isn't going to be pretty ... but a win's a win," Orton told reporters.
Chicago's stellar defense gradually stifled Green Bay, giving Orton the chance to launch a last-ditch attempt to save the season.
"Defensively, we played hard through the game. The guys played hard, hung in there, and played the run and the pass," said Bears coach Lovie Smith.
Fighting back
Chicago started their comeback early in the third quarter with a 3-yard Orton pass to tight end Greg Olsen that capped off a 27-yard, five-play drive. Orton finished with 14-27 passes completed for 142 yards.
Running back Matt Forte tied the game with three minutes remaining with a 3-yard touchdown run, after Chicago secured a critical first-and-goal by inches. Forte's 73 yards of rushing elevated him to a team rookie rushing record.
"When your back is really up against the wall, the best comes out. For our season to continue the offense needed to make a stand, and they did," said Smith.
If Gould was the hero, his Packers counterpart Mason Crosby was the villain.
Crosby had a chance to win the game with a 38-yard field goal attempt seconds before the end of regulation, but Chicago defensive end Alex Brown blocked the kick.
"Our season was on the line. We had to block the kick, and Alex Brown came through as he's done so many times," Smith said.
The Bears' sense of destiny grew when they won the coin toss for overtime and quickly drove deep enough into Green Bay territory to entrust the game to Gould.
"We know his range," Orton said of the kicker.
Packers quarterback Aaron Rodgers looked strong in mounting two long touchdown drives in the second quarter: 91 yards in 14 plays, and 58 yards in six plays.
But the Packers lost their way as the long, cold night wore on. "You have to play two halves," Smith said. "In the second half the team really came through."