The pass from Sam Bradford was the sixth grab of the game for Gibson, who ended with 100 receiving yards as the Rams (6-6-1) logged a third straight win for the first time in six years.
Bradford finished 19-of-39 through the air for 209 yards, a touchdown and an interception for St. Louis, which trailed 6-0 at halftime.
Steven Jackson paced the Rams' rushing corps with 64 yards and a touchdown on 19 carries.
The Bills (5-8) were led by Ryan Fitzpatrick (25-of-32, 247 yards, one touchdown, one interception).
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