The 2008 champions scored three tries in 13 minutes - two from full-back Leigh Halfpenny, who finished with 22 points - to set up an intriguing Twickenham clash against unbeaten rivals England later this month.
Wales were held 3-3 at the interval, but Scotland could not live with the pace, power and purpose of their opponents during a damaging third quarter as Halfpenny twice and wing Alex Cuthbert touched down in rapid succession.
During that same period, Scotland were briefly - and critically - reduced to 13 men after centre Nick De Luca and full-back Rory Lamont received yellow cards for tackling players without the ball, although they did ultimately manage a first try in five Tests when fly-half Greig Laidlaw crossed.
Laidlaw converted his try and added two penalties on a promising full debut, yet World Cup semi-finalists Wales were in a different class once they hit their straps.
Halfpenny only missed one kick at goal, and Wales have now scored 50 points and six tries in two Six Nations games this term, which suggests England will have their work cut out to prevent them from clinching the Triple Crown.
Wales even prevailed without captain Sam Warburton, who failed a fitness test on his leg injury suffered last weekend, which meant a surprise Test debut for Scarlets flanker Aaron Shingler.
Hampshire-born Shingler, whose brother Steven was named in Scotland's Six Nations training squad despite eligibility doubts now being probed by the International Rugby Board, rocketed straight into Wales' starting line-up.
Ryan Jones, meanwhile, equalled Ieuan Evans' Wales record of 28 Tests as captain, taking over from banned lock Bradley Davies, and key World Cup forwards Gethin Jenkins and Dan Lydiate returned from injury after missing last weekend's Six Nations opener.
Scotland, without a win at the Millennium Stadium since 2002, handed Laidlaw their number 10 shirt following Dan Parks' retirement from Test rugby five days ago, and prop Geoff Cross replaced Euan Murray, who does not play on Sundays for religious reasons.
The stadium's closed roof guaranteed perfect playing conditions, unlike in Rome and Paris yesterday, and both sides looked to play at a searing tempo.
Laidlaw missed an early penalty chance, yet Scotland readily freed strong-running forwards Richie Gray and David Denton, refusing to play second fiddle during a frantic opening.
Scotland enjoyed plenty of possession, helped by a misfiring Welsh lineout, but much of the action was centred around halfway and genuine try-scoring opportunities were at a premium.
Laidlaw kicked a 22nd-minute penalty from close range, and the visitors probably deserved it on the balance of play, with Wales sometimes exercising wrong options.
Halfpenny, retained as first-choice goalkicker following his late heroics in Dublin, drew Wales level 10 minutes before half-time through an effortless strike from 40 metres, but Scotland continued to mix it strongly in all areas.
They should have scored just before the interval, going through 21 phases of play, but possession was knocked on just when it looked as though Wales had run out of defensive numbers.
A team harbouring greater attacking confidence than one that had gone four successive Test matches without scoring a try would undoubtedly have made it count, yet Wales escaped.
The home side suffered a major blow, though, when wing George North limped off nursing an ankle injury, being replaced by James Hook, with Halfpenny taking North's wing slot.
It was a scrappy, largely patternless opening 40 minutes, and Wales knew they had to move up at least two gears after being held 3-3 by a team largely written off before the start.
Wales coach Warren Gatland clearly gave his team a severe half-time lecture, and it had the desired effect as Scotland unravelled in alarming fashion.
Scrum-half Chris Cusiter made a hash of gathering the kick-off, and Wales pinned Scotland back from an attacking lineout, working the attacking angles until Hook sent Cuthbert galloping over.
Halfpenny converted, and Scotland kept their finger on the self-destruct button when De Luca tackled Davies without the ball and referee Romain Poite yellow-carded him on assistant Simon McDowell's recommendation.
Laidlaw briefly reduced Scotland's deficit through his second penalty, but rampant Wales then struck again after more patient attacking play saw Halfpenny score, and then he struck again just five minutes later.
Scotland were at sixes and sevens, and with Halfpenny also kicking 12 points, Wales had done the damage - despite a late yellow card for Jenkins - and they will head to Twickenham in 13 days' time quietly confident of completing stage three in a possible third Grand Slam season in eight campaigns.
PA
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