Murray, the first Scottish player to be red-carded in a Test match since 2002, departed after just 22 minutes, with New Zealand referee Steve Walsh also sin-binning Gough for a late tackle on Murray.
Scotland, who had conceded a sixth-minute penalty try when Wales exerted scrum dominance, battled bravely to stay in touch.
But Wales' one-man advantage inevitably told, and skipper Gareth Thomas claimed a try double, taking his Test tally to 36, while lock Robert Sidoli also touched down, with fly-half Stephen Jones slotting four conversions.
It was a satisfactory Welsh response to their 47-13 drubbing against England at Twickenham last Saturday.
Although Scotland managed late consolation tries from full-back Hugo Southwell and wing Chris Paterson, who also kicked two penalties and a conversion, main line-out operator Murray's departure left a huge void.
Wales attempted to produce their renowned wide game, and with scrum-half Dwayne Peel the architect of those confident attacking efforts, Scotland were ultimately run to a standstill.
Scotland's defeat means England - who visit Murrayfield when the tournament resumes on February 25 - are Six Nations leaders by two points, and now the only team who could clinch a Grand Slam this season.
Wales, meanwhile, will travel in confident mood to Dublin, where Ireland await in a fortnight.
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