Playing with a fierce wind at their backs from the River Taff end, Richard Whiffin’s side made full use of the conditions.
Fly-half Carwyn Leggatt-Jones was ruthless from distance, drilling three long-range penalties to help establish a commanding interval lead.
There had been four changes to the side that pushed England and France close in the opening rounds, and the hosts burst out of the blocks.
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Towering lock Luke Evans powered over in the sixth minute after slick interplay between forwards and backs carved open the visitors.
Leggatt-Jones failed to convert but quickly made amends, punishing a Scottish offside with a 48-metre strike before landing an even longer effort from near halfway soon after.
The scoreboard kept ticking when debutant centre Bailey Cutts sliced through off an inside ball from Tom Bowen to make it 16-0 inside a quarter of an hour.
Scotland eventually found some rhythm, tightening up defensively and building pressure from a line-out deep in Welsh territory.
A rolling maul drove towards the line and scrum-half Hamish MacArthur appeared to have touched down.
Although initially awarded, the score was overturned after the TMO spotted a neck roll in the build-up — a let-off for Wales.
Leggatt-Jones had the final word of a scrappy closing spell, slotting a 42-metre penalty to send the hosts into the break 19-0 ahead — a margin slightly healthier than the 16-point cushion they held against England earlier in the campaign.
The next score always felt pivotal. Scotland thought they had one early in the second half but were held up over the line.
Moments later they did strike, centre Campbell Moore finishing sharply near the posts after inventive handling from a five-metre line-out. MacArthur converted and the deficit was cut to 12.
Wales needed a response and it came from co-captain Deian Gwynne, who delivered a dynamic display that later earned him player-of-the-match honours.
He claimed clean line-out ball at the front and surged into the 22, sparking a multi-phase assault.
Gwynne carried again as the move swept left, and when the ball was recycled, Leggatt-Jones delivered a pinpoint cross-kick for debut wing Dylan Scott to gather and score in the corner.
The bonus-point try followed on the hour. Hooker Tom Howe bulldozed over from close range and replacement fly-half Lloyd Lucas added the extras to stretch the advantage to 31-7.
Scotland rallied late on. Replacement Jack Marshall crossed, followed by Jackson Rennie, with Jake Dalziel converting both to narrow the margin to 10 points. But Wales had done enough.
After narrow losses in the opening rounds, this was the breakthrough they needed — clinical with the wind, resilient when tested, and finally rewarded with a bonus-point win to kick-start their campaign.
