The Scots, cock-a-hoop after beating tournament favourites France last weekend, crashed back to earth after lock Scott Murray was sent off for kicking Wales forward Ian Gough in the head.
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.