Manuel completed 10-of-22 passes and overcame a pair of pick-offs as the Bills (2-2) shook off a loss to the New York Jets last week.
Woods finished with four grabs for 80 yards while Fred Jackson carried the ball 16 times for 87 yards and a score in the victory.
C.J. Spiller also supplied rushing support, gaining 77 yards on 23 carries for Buffalo.
The Ravens (2-2) saw their two-game winning streak snapped as Joe Flacco tossed five interceptions for the first time in his career. He went 25-of-50 through the air for 347 yards and two touchdowns in the loss.
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