Following a first half played in a driving snowstorm, the teams combined for five touchdowns in the final 125 seconds. Brown's catch concluded a five-play, 80-yard drive that took 41 seconds.
Baltimore (7-6) has its first three-game winning streak this season and the inside track for the second AFC wild card.
Minnesota (3-9-1) lost Peterson in the second quarter with an ankle injury.
Copyright 2013 by The Associated Press