Former Dynamo defender Patrick Ianni struck the winner with a spectacular overhead effort, which sees the Sounders now just three points behind Western Conference-leading Houston.
Seattle coach Sigi Schmid said: "They worked their hardest and that's all we can ask for when they step on the field. Sometimes it's a lot to overcome and it was too much today. I think at the end of the game, we were pushing hard and trying to get a result out of it and came close on a number of occasions. It's a tough place to play and it's a good team they have. They work a lot of things in their favor and they came out with the win."
Meanwhile, Ianni was the hero of the 32,404 home crowd at Qwest Field and added: "Obviously I've never practiced that or anything.
"You just do your best to put it on the frame and, fortunately, it went in. I think we deserved it today, but it came in a not-so-conventional way.
"Basically it's special because they're in first place right now. I want to give this team as much as I can. I haven't been with [Houston] for a while now, so I'm not holding too much of a grudge. They taught me a lot when I was down there and I'm just happy the work I put in down there is coming in handy here in Seattle."