Wales were cruising to a fourth win out of four when at halftime they led 15-6, a scoreline that flattered the Scots, who were coming off two bumbling losses to Ireland and France.
Then Scotland suddenly came alive to own the second half. Grant Gilchrist was held up over the line, then Darcy Graham finished a brilliant backs move, and Scotland trailed by only four with 22 minutes to go and their crowd roaring them on.
Scotland virtually owned the half, playing with all of the ball, forcing penalties, and pinning Wales down. But the Scots kept ruining their progress with errors, a spill or poor pass or turnover. Wales' renowned defence also came to the fore, as it made 138 tackles in the second half after 66 in the first.
A compelling match finished with Scotland, exhausted and frustrated and patched together, back in its 22 for the first time since the end of the first half, and Wales flyhalf-cum-fullback Gareth Anscombe kicking a second penalty to complete its record-extending 13th straight win.
Despite distractions at home regarding an overhaul of clubs, Wales will play defending champions Ireland next Saturday in Cardiff for their first Grand Slam since 2012, and a first Six Nations crown since 2013.
All of Wales' seven previous tries in the tournament came after halftime, but wing Josh Adams was over after just 13 minutes. Jonathan Davies gave him the overlap with a forward pass that wasn't picked up until video replays, and Adams shimmied past Blair Kinghorn to score behind the posts.
The battering was also physical. Backup hooker Fraser Brown was playing flanker after Jamie Ritchie and temporary replacement Hamish Watson took head knocks. Then wing Tommy Seymour left holding his arm.
A Graham break earned a second penalty kick by Finn Russell, but Anscombe pushed Wales further ahead with a penalty, though he couldn't convert Jonathan Davies' try after a coolly composed 24-phase buildup that was reminiscent of Wales' match-turning 35-phase try against England two weeks ago. The buildup, dominated by the forwards, featured two big crashes into the defense by Davies' midfield partner Hadleigh Parkes.
The try also injured Scotland fullback Kinghorn, bringing on Adam Hastings, their third flyhalf on the field.
Wales almost finished the half with more points, but an Anscombe penalty into the sun rebounded off the left post, Parkes regathered, and Adams knocked on to end the chance. That was Wales' first handling error of the half, at which point Scotland was game as usual but outclassed.
But Wales became the punching bag in the second half.
Scotland took better care of the ball, and also didn't.
A surge by prop Allan Dell died after Russell threw a pass over the sideline.
From an attacking lineout, Gilchrist was held up over the line by Parkes.
Another sustained Scotland attack featured stops by Parkes on Graham, and Dan Biggar on Hastings, before the home side conceded a penalty.
With all of the errors, Scotland's try came as a slight surprise. A rolling maul drew in the Welsh defense, a Russell inside pass to Byron McGuigan put the replacement wing in space, and Hastings sent Graham diving into the right corner.
Scotland was back with more than a quarter left, but it couldn't finish off Wales when it had chances.
Ball was knocked on or passes dropped, soft penalties given up, and an 18-phase play finished with a turnover. Wales gratefully accepted each relief, and a 12th win over the Scots in their last 13 matchups.