The non-conference meeting of the two teams marked the third time the Rams had set foot in upstate New York in 27 years.
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The visit started off with a lackluster first half for the Rams, during which time the Bills held a wide lead, with 21-3 on the scoreboard by halftime.
By the third quarter, that lead was extended by Stephon Diggs with a four-yard touchdown pass from quarterback Josh Allen.
That seemed to stir some life into the Los Angeles team, which then scored two consecutive touchdowns, closing the gap 28-17. The Ram's secondary had been a strength during the previous two games.
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Then, with roughly 10 minutes left in the final quarter, Jared Goff threw a 16-yard pass on a two-point conversion attempt and succeeded, closing the gap 28-25.
With less than five minutes left in the game, Darrell Henderson Jr. completed a one-yard rush for the Ram' first lead in the game.
That was before Josh Allen's 13-yard touchdown pass to Tyler Kroft with 15 seconds left that gave the Bills a 35-32 victory. Allen threw four touchdown passes and ran for a fifth score as the Bills remained unbeaten.
The Associated Press contributed to this report.