The 11-5 Vikings shut out their visitors for the opening three quarters, but the Seahawks made the final period count to set up a divisional-round match with the Carolina Panthers next weekend.
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Temperatures plummeted below zero in one of the coldest NFL games ever played, and that had an impact on the play as both sides struggled to get going on offense.
The first points arrived late in the opening quarter when Blair Walsh knocked over a 22-yard field goal after a combination of Teddy Bridgewater and Adrian Peterson had got the Minnesota Vikings within range.
The second quarter passed scoreless, however, and the combined total of 185 yards made between the two sides was the lowest in the first half of a playoff game since 2005.
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Matters didn't improve much in the second half either, although the Vikings did double their advantage when Russell Wilson's interception allowed Bridgewater and Peterson to again set up a Walsh field goal.
A third Walsh kick nudged the hosts into a nine-point lead, but Seattle finally hit back in the fourth quarter when Wilson picked out Doug Baldwin with a three-yard pass into the endzone for the only touchdown of the contest.
The Seahawks won the ball back almost immediately when Kam Chancellor stripped Peterson of possession, and that allowed Steven Hauschka to kick his side in front for the first time with a 46-yard field goal, keeping alive their hope of reaching a third consecutive Super Bowl.
The Vikings had one last chance to nick the victory in the dying stages when they set up a field goal just 27 yards from the post, but Walsh dragged his effort wide left to condemn his side to an early playoff exit.