Folk got a second chance after he missed a 56-yarder moments earlier. But Chris Jones was called for unsportsmanlike conduct for pushing a teammate forward to try to block the kick, a new NFL rule.
New York, given new life, ran the ball three times to set up Folk's winner.
New England had defeated New York in six straight regular-season meetings. The loss also ended New England's 12-game winning streak against the AFC East.
Copyright 2013 by The Associated Press