But with Jones missing both conversions, they had to settle for a 13-0 lead.
Scotland's record points-scorer, Chris Paterson, a surprise omission from the starting XV, made the most impact for Scotland on his arrival for the injured Webster.
First he clawed three points back from a penalty, taking his tally to 696 in Test rugby, and then came within inches of the try-line with a dartinf run as the first half drew to a close.
But Wales were able to soak up the pressure and finish the half with another three points from Jones when Scotland were penalised for handling in the ruck.
It took just 48 seconds after the restart for Wales to extend their 16-3 lead with a third try, sparked by a great Jamie Roberts run through the Scottish defence.
Leigh Halfpenny claims Wales' third try on his Six Nations debut
The ball was switched to the right and Shane Williams off-loaded in the nick of time to Cardiff Blues wing Halfpenny, who dived over in the corner on his Six Nations debut. Jones once again failed with his kick.
Paterson did reduce the deficit to 21-6 with a penalty after Wales number eight Andy Powell had his hands in a ruck.
But Scotland were not really testing the Welsh defence and a fourth try for the visitors followed just before the hour.
Jones off-loaded to Roberts as play was switched left before the ball eventually arrived in the hands of Shane Williams two metres out.
The diminutive wing promptly dived through a gap to record his 45th Test try, passing ex-All Blacks wing Jeff Wilson on the all-time list.
Martyn Williams was sin-binned with 13 minutes left for deliberately knocking on in a tackle, allowing Scotland to apply some late pressure.
The hosts made the most of it when replacement Evans scooted round Shane Williams, who then went off with a foot injury, and inside Byrne after some good build-up work.
Paterson converted and almost grabbed a second Scottish try two minutes from time when he dived for the ball with Byrne, but the television match official confirmed that he had not applied downward pressure.
Scotland: Southwell, Webster, Cairns, Morrison, Lamont, Godman, Blair, Jacobsen, Ford, Cross, White, J Hamilton, Hogg, Taylor, Barclay. Replacements: Paterson for Webster (21), Dickinson for Cross (31), M Evans for Cairns (52), Gray for Barclay (56), Cusiter for Blair (62), Hall for Ford (62), Brown for Hogg (73).
Sin-bin: Cross (20)
Wales: Byrne, Halfpenny, Roberts, Shanklin, S Williams, S Jones, Phillips, Jenkins, Rees, A Jones, Gough, AW Jones, R Jones, M Williams, Powell. Replacements: Peel for Phillips (60), Bishop for Roberts (63), Hook for S Jones (63), Yapp for Jenkins (63), Bennett for Rees (63), Charteris for Gough (63), Davies for S Williams (72).
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