The hosts struggled to get into gear in the opening stages of the game, kicking out on the full and almost being caught out by Richie Gray's surge through the middle.
Scotland continued to press against their opponents but were caught out on six minutes when Gareth Davies intercepted outside his own 22 and raced the length of the pitch to score in the corner.
Leigh Halfpenny added the subsequent conversion to edge Wales ahead against the run of play, and things would get even better for the Dragons as the 29-year-old crossed over on 12 minutes before adding two more points from the boot.
The first half ended 14-0 as Wales took all their opportunities while Scotland spurned their chances despite enjoying more possession.
Scotland then shot themselves in the foot early in the second half by giving penalties away on 43 and 48 minutes, which Halfpenny successfully struck to add yet more points to his tally.
There was no let-up for the visitors as they continued to be shut out by Wales, who in turn added two more tries and two more conversions.
Halfpenny crossed over just after the hour and Steff Evans touched the ball down with a one-handed finish on 73 minutes to leave Scotland facing humiliation.