New England started fast as Tom Brady found Danny Amendola for a touchdown in the first quarter, before stretching their early lead to 15-0 when Rob Gronkowski got his name on the scoresheet soon after.
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Pittsburgh responded before the break with their first score of the night that was well taken by Antonio Brown, but Stevan Ridley's drive into the end zone with 13 seconds left in the first half restored New England's two-touchdown advantage.
From that point on the Patriots took complete control of a high-scoring second half, with Aaron Dobson's brace the highlight of a four-touchdown effort in the fourth quarter.
Despite Cotchery completing his hat-trick, Pittsburgh had no answer to Brady's accuracy late on, falling to a sixth defeat of the season despite Roethlisberger throwing 400 passing yards for four touchdowns.