The City midfielder laid on the best chance of an evenly-matched first half when she squared for Erin Cuthbert, but her vicious effort smacked off the underside of the Welsh crossbar on the stroke of half-time.
However, the Chelsea midfielder wasn’t to be denied a second time, picking the pocket of Wales goalkeeper Laura O’Sullivan to tap in an absolute gift just before the hour
The hosts rallied after that setback in search of the equaliser, but it ultimately proved elusive as Scotland held on for a deserved win.
It provided the perfect early birthday present for Weir, who herself grabbed the winner against Northern Ireland in her national team’s last outing.
The midfielder turns 26 this Sunday and will already have one eye on this summer’s Olympics, when she joins nine of her City teammates as part of the Team GB squad.
Hege Riise’s side face Zambia in a friendly at Stoke City’s Stadium on Thursday 1 July, with their Group E opener coming 20 days later against Chile.
Host nation Japan and Janine Beckie’s Canada make up the rest of the Group, with Great Britain locking horns with the pair on 24 and 27 July respectively.