Stafford finished with four scoring strikes in all, going 25-for-43 through the air for 248 yards with an interception as the Lions (4-2) rebounded from a loss to Green Bay last week.
The Browns (3-3) saw their three-game winning streak snapped as Brandon Weeden was intercepted twice. He completed 26-for-43 passes for 292 yards and two touchdowns.
Josh Gordon made seven catches en route to 126 yards for Cleveland.
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