Vale were tremendous in the opening half hour when the acrobatics of Dorus de Vries kept the runaway leaders on level terms.
He produced a fine save to keep out Chris Herd's shot and topped that with a stunner to keep out a 13th minute header from David Howland.
Luke Rodgers also made a mess of a gilt-edged opportunity for Vale with the Swansea defence all at sea.
The visitors showed signs of riding the storm towards half-time as Scotland's shot was blocked and a free-kick from Ferrie Bodde was deflected over the top.
And another free-kick provided Swansea's first serious threat when Andy Robinson's effort was saved at full stretch by Joe Anyon.
A Robinson shot was also tipped to safety at the start of the second period with the visitors finally stringing their passing game together.
And Swansea took the lead with a highly debatable penalty decision in the 63rd minute.
There were no appeals as Robinson went to ground under the challenge of Dave Mulligan, but referee Ray Lee pointed to the spot and Scotland converted with ease.
The decision infuriated the home crowd and Scotland rubbed salt in Vale's wounds with a fortunate second goal 15 minutes from time.
Thomas Butler's shot cannoned back off a post and the ball rebounded off Scotland before rolling into the net.
Vale kept plugging away in a forlorn attempt to find a way back and Mulligan's free-kick was floated harmlessly over the top to sum up their disappointing day.
Swansea were able to coast the final stages and could even have added a third as Anyon saved well from substitute Febian Brandy.