A 64th minute try by centre Jonathan Davies has helped Wales overcome the challenge of a spirited Scotland side 26-23.
The Clermont Auvergne midfielder burst through the home defence to score under the posts and effectively settle the tight contest in favour of the Welsh, who lost their opening night home fixture against England 21-16.
The victory maintained Warren Gatland's record of never having lost to Scotland in eight seasons as Wales' head coach.
Scotland scrum-half Greig Laidlaw felt the referee finished the game slightly early, robbing the Scots of a chance to snatch a late win.
"Disappointed to come up short, we played some good rugby but came up short," he told the BBC.
"Rome was not built in a day, and this team is on a journey with (coach) Vern Cotter. I thought the referee forgot how long was on the clock at the end."
Wales lock Alun Wyn Jones felt his side still hadn't clicked into top gear.
"We were unconvincing last week, and again towards the end today but a win's a win," he said.
"In the last couple of games we've been unconvincing but credit to Scotland, they never gave up."
Wales now move on to two points from two matches, two behind England and defending champions Ireland, who are both unbeaten and meet each other on March 1 in what could turn out to be the championship decider.
Wales now travel to Paris to face France while Scotland welcome Italy in a match that will likely decide the tournament's wooden spoon as both sides have yet to secure a point.
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