Dan Biggar's drop goal had broken a 6-6 deadlock but on 75 minutes Seymour raced clear to dot down meaning the Warriors stay fifth in the table but are now only a point behind their Welsh opponents with two games in hand.
And Townsend admitted afterwards that his side had drawn on all their guts and determination to grind out a victory.
"Relief is one emotion," he said. "I am full of joy at seeing the team doing so well in difficult circumstances when you go behind against such a good team with a few minutes to go.
"They fought for that win and showed real belief to get that win. It was a great finish and when you get a break like that, it is a great bit of skill by Niko to put the kick in, but you need someone to go and finish it and Tommy did very well.
"I thought defensively we had a few missed tackles tonight that we've not seen for a while.
"But the important thing is the character the team showed to keep our line intact and a belief we can win."
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