Running back Tyrell Sutton caught a short pass from Russell Wilson and took it 34 yards up the sideline for the touchdown, giving the Seahawks a 25-10 lead.
The run capped off an 85-yard drive that also included a 22-yard pass-and-catch from Wilson to tight end Sean McGrath.
Early in the fourth quarter, Osweiler remains at quarterback as the Broncos begin the ensuing drive.