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There was bad news for the AFC West side later in the quarter though, as running back Danny Woodhead was ruled out for the remainder of the game with an apparent ankle injury.
Nick Novak kicked a pair of field goals to extend the visitors' advantage, while Bills quarterback EJ Manuel looked for Sammy Watkins just before the break, but the rookie wide receiver could not hold on to the pass.
Royal continued to get the better of the Buffalo defense at the start of the second half, as he hauled in a Rivers pass out wide before sprinting down the sideline for his second touchdown of the day.
Fred Jackson collected a short pass from Manuel late in the third quarter to give the home side some hope, but they were unable to carry their momentum into the final 15 minutes.
The result ends the Bills' unbeaten start to the season, leaving both teams with a 2-1 record.