The opening goal was man of the match Routledge's first league goal of the season for the Swans.
He told Sky Sports 1: "It was long overdue.
"But it was obviously a massive game today and everyone knows what it means to the fans and the city. It's an important goal, and important game and a more-important three points.
"It's a massive result, three points from a derby game, and we hope to kick on from here and take that into the next match."
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