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However, the Vikings responded and took the lead when Christian Ponder tossed the ball to wide receiver Cordarrelle Patterson on a run play and he ran right through several tackles to sprint into the endzone for the 33-yard score.
The Bears hauled the Vikings back just before the break when Gould was again brought into action and he dispatched a 40-yard field goal through the posts to bring his side within a point.
After the break, the visitors took the lead immediately as McCown fired downfield to Alshon Jeffrey and he ran all the way into the endzone bouncing off two tackles to coast in for the 80-yard score.
The Vikings hit back with a field goal through the leg of Blair Walsh from 32 yards, but the Bears came right back at the home side with another score.
McCown found Jeffrey again down the left sideline and he somehow held the ball and fell face first into the endzone for the 46-yarder touchdown.
Minnesota took their time to rally being led by backup quarterback Matt Cassel after Ponder left the game with a concussion, but he got his side back into the game with a brilliant throw to the endzone and Greg Jennings made a good catch to keep both feet in bounds for the 15-yard strike.
With 30 seconds left in the contest, the Vikings tied the score as Walsh fired a kick between the posts from 34 yards to send the match into overtime.
Leslie Frazier's side moved into field goal range and Walsh thought that he had delivered the game-winning kick from 39 yards, but it was ruled out due to a facemask penalty, which moved them back 15 yards and his effort from 57 missed.
That allowed the Bears to engineer a drive of their own and Gould was brought on to kick from 47 yards to seal the game for his side, but he saw his effort miss as well handing the initiative back to Minnesota.
This time the Vikings did not slip up as Adrian Peterson moved them into a close range for Walsh and he made no mistake from 34 to earn his side the victory.