The Patriots (2-2) were trailing by 14 points in the third quarter but then turned it on, finding the end zone on six of their next seven possessions.
Brady struck for 340 passing yards and was helped by a running game that saw Brandon Bolden and Stevan Ridley team up for 243 yards and three touchdowns.
Buffalo (2-2) got 350 aerial yards and four TD passes from Ryan Fitzpatrick, but the Bills signal-caller was intercepted four times.
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