© PA Photos
A frantic finish to the first half saw more penalties, with Wales taking a single-point advantage at the break.
With try-scoring opportunities at a premium, the home side relied on Laidlaw to add to their score, but the fly-half missed his opening effort at the uprights.
Halfpenny put his first-half accuracy problems behind him adding 15 points with the boot in the second half for Wales, helping the reigning Six Nations champions to a 10-point lead with eight minutes to go.
Scotland had a chance to reduce Wales's lead late on, with Paul James sent to the sin bin for holding on, but the home side conceded a penalty, allowing Wales to secure the win.
The game has set a new record for most penalties scored in a Six Nations match.