Barnes opened the scoring in the 17th minute after Will Bruin had drawn goalkeeper Michael Gspurning out of position. He instead sent a pass to Barnes, who fired into the open net for his first goal since early May.
He doubled the advantage 4 minutes later with his sixth goal of the season, connecting from long range over Gspurning.
Bruin also scored as the Dynamo (10-7-6) retained their Eastern Conference playoff spot.
Shalrie Joseph scored for the Sounders (10-8-4), who remained on the outside of of the West's post-season picture.