Edwards hit rookie James Hardy on a 7-yard scoring play with 4:10 remaining. The Bills quarterback finished the contest with 20 completions for 239 yards.
Marshawn Lynch carried 19 times for 59 yards and a touchdown for Buffalo (2-0).
Jacksonville's David Garrard passed for 170 yards and was intercepted once.
Maurice Jones-Drew ran for a touchdown and Fred Taylor carried 14 times for 49 yards for the Jaguars (0-2).
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