In the second half Taylor Paris, Fraser Thomson, Josh Strauss and Tim Swinson, who crossed twice, added touchdowns for the Scottish outfit who recorded the RaboDirect PRO12's largest ever away win.
Duncan Weir converted five tries and kicked two penalties while Scott Wight converted two with Tom Prydie's penalty little consolation for the Welsh region.
"It's hard to get our heads round it," said Townsend, who also claimed the club's largest ever league win.
"We'd prepared really well for a very tough game. We realised that no Scottish team had won down there in the Rabo in five seasons.
"It was one of those nights when we came out with good intent in defence and attack and everything clicked.
"The way Dragons had been playing in recent weeks we knew it would be a tough game," added Townsend, in his first season with Glasgow.
"When you get to a stage where you get three or four tries and you've won the game, the opposition force things and we capitalised on that and played some really good rugby in the last 20 minutes.
"I am really proud of the players and delighted for them. They have worked really hard throughout this season.
"We knew a game like that was hopefully going to come this season."
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