Swans took the lead after 12 minutes at Merland Rise, Max Hustwick glancing in a header from a right-side corner.
After dominating the first-half they were unfortunate to be pulled back five minutes before the break when a mix-up in defence led to a clearance hitting Max and the ball rebounding into his own net.
But they got what proved to be the winner after 72 minutes when Darren Simpson finished neatly from a left-side cross.
