Albion lead Swansea in the Carabao League Cup with both goals coming from a seemingly rejuvenated Aaron Connolly.
The first was a deflected effort past Steven Benda and the second came after a sublime pass from Alexis Mac Allister.
Connolly angled a drive into the bottom corner.
Swansea had early efforts through Liam Cullen and Morgan Whittaker although both were well saved by Albion captain for the night Jason Steele.
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