This latest win means that Bath – who came desperately close to relegation last season – now have an unbeaten record in the 2003/04 season to date, a remarkable turnaround in fortunes.
But they certainly left it late to rescue this result, Barkley's winning penalty coming from a thrilling last ditch assault on the Wasps tryline which saw wave after wave of attack creating panic in the home side's ranks.
Demonstrating superb close contact skills, Bath won ruck after ruck, stringing together a total of 14 phases of play to stretch the Wasps defence to breaking point.
Just when the men from the West Country looked poised to score, Wasps lock Simon Shaw – a first-half hero having scored a well-taken try – interfered with Bath possession right in front of his own posts to give away the crucial penalty in the 80th minute.
As the England reject took his place in the sin bin, Barkley was able to land the simple penalty to dash the champions' hopes of gaining a badly-needed victory.
With Wasps defending a 19-14 lead going into the last quarter, it had looked as if Wasps would be able to ride out the Bath fightback, Barkley missing an eminently kickable penalty in the 61st minute and Wasps generally controlling every facet of play.
The trusty boot of Wasps fly-half Mark van Gisbergen – allied to Shaw's try in the 10th minute – had ensured the home side were in the driving seat for the final exchanges but Bath had other ideas and finished the stronger side.
With winger Brendon Daniel grabbing two tries in the opening quarter, Bath continued to play enterprising rugby, finding holes in the Wasps defence throughout the encounter.
Indeed, Daniel came very close to getting his hat-trick late in the second half following a superb break from team-mate Jamie Williams, but the winger was bundled into touch after a great cover tackle from Tom Voyce in the left hand corner.
Wasps cleared their lines but moments later found their lead cut after back rower Peter Scrivener was penalised in his own half. That enable Barkley to land his first penalty kick of the afternoon and put the visitors within two points of their opponents and set up the thrilling finish.
For Wasps: Tries: Shaw Cons: Van Gisbergen Pens: Van Gisbergen 4
For Bath: Tries: Daniel 2 Cons: Barkley 2 Pens: Barkley 2