Steven Hauschka got the only points of a quiet first quarter, kicking a 39-yard field goal to give his side a three-point lead.
He added a second kick from 43 yards early in the next quarter before Matt Bryant responded with one of his own from 53 yards to reduce the deficit back to three.
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Hauschka added another kick with just under two minutes to play before Golden Tate capped off a lucrative spell with a one-handed catch from Wilson's looping pass into the end zone with just eight seconds of the half left.
Another field goal midway through the third quarter extended the Seahawks' lead even further, but the Falcons responded with a touchdown late in the same quarter when Matt Ryan picked out Darius Johnson with a 12-yard pass.
Seattle regained their 23-point lead in the fourth quarter when Marshawn Lynch made his way around the defence from a yard out to make it 33-10 to the visitors, and that was how it finished as the Seahawks moved to 9-1 for the season.