Arguably it was Wales’ worst performance of the opening three rounds but they still had enough to avoid only a second home Six Nations defeat to the Scots.
The visitors, who started with an impressive win in Italy and then pushed England hard, will lament missed opportunities when they had the wind at their backs.
With both head coaches of the senior teams, Steve Tandy and Gregor Townsend, in attendance it was the hosts that started sharply.
They were 11-0 up after 12 minutes thanks to Exeter lock Evans going over from close range and a pair of booming penalties by Leggatt-Jones.
The second try came in the 16th minute after fast hands released Tom Bowen down the left and the wing stayed calm to put centre, and Cardiff clubmate, Cutts over for a try on debut.
Scotland needed a response but were denied one when a try from a snipe by scrum-half Hamish MacArthur, one of nine Edinburgh players in the XV, was chalked off due to a neck roll in the build-up.
The final act of a scrappy first half was a third Leggatt-Jones penalty to stretch the lead to 19-0.
The Scots were held up over the line soon after the restart but then went over through Glasgow centre Waugh from a neat offload by rangy fly-half Jake Dalziel.
Scrum-half MacArthur converted to make it 19-7 but Wales caught the visitors cold with a rare attacking foray in the 52nd minute.
Impressive captain Deian Gwynn burst into the 22 from a cunning line-out move for Leggatt-Jones to find the unmarked Scott with a cross-kick that the debutant did well to gather in the challenging wind.
The nerves were settled and Wales sealed victory on the hour when hooker Howe, their star of the tournament so far, barged over.
Scotland finished hunting a pair of bonus points thanks to tries by Marshall and Rennie but late chances went begging and it was a pointless trip.