The inspirational Jones surpassed Richie McCaw's tally at Parc y Scarlets, but he was unable to mark the occasion with a win.
Rhys Carre scored the game's opening try for Wales when he wriggled through between the posts in the first half, with Scotland just a point behind at the break after penalties from Finn Russell and Adam Hastings.
Yet poor discipline in the scrum cost the 2019 Grand Slam winner, aa Stuart McInally pounced to score Scotland's only try and Stuart Hogg landed another penalty from the last kick of the game to seal Scotland's first Six Nations win in Wales since 2002.
Leigh Halfpenny's penalty with 15 minutes to go had set up a tense finale, but Wales finished second bottom of the table after a fourth loss in five Six Nations matches.
Scotland hit the front inside 10 minutes, as Russell converted after Ryan Elias was penalised for offside.
Chris Harris should have taken in Hogg's pass in the 20th minute, but a fumble from Scotland's number 13 allowed Dan Biggar to intervene.
Scotland was made to pay just after the half-hour. With the wind causing havoc at lineouts, Elias nipped in to steal possession, and Carre bundled his way over under the sticks – Biggar adding the extras.
An injury to Russell compounded Scotland's frustration, but a penalty from his replacement Hastings reduced the deficit to one point at the break.
A collapsing Wales scrum gave Scotland a golden opportunity with 20 minutes remaining and Gregor Townsend's side swiftly capitalised – McInally grounding off the back of a driving maul.
Hastings's failed conversion handed Wales a reprieve, with Halfpenny kicking it to within a point, but Hogg put the icing on the cake right at the end as Scotland won a third successive Six Nations match for the first time since 1996.
Wales has now lost its past five matches, including three at the start of the Six Nations earlier in the year, and its defeat to France last time out.
The 2019 Rugby World Cup semi-finalist put in a disappointing defence of its title and having replaced Warren Gatland, Wayne Pivac will be searching for some much-improved displays from his side in the upcoming Autumn Nations Cup.
Scotland is set to face Italy in the Autumn Nations Cup on 15 November, a day after Wales goes up against Ireland.