A first half goal from the visitors was the only goal of the match in front of 827 fans at Jenner Park.
After half an hour of play, a free-kick from the right caused chaos in the Barry defence, leading to an attempted clearance rebounding off Ferry’s Cullen Kinsella into the net.
From then on, the visitors adopted a defensive formation, with Barry pushing forward for an equaliser.
Callum Sainty hit the post twice for Barry, while Kayne McLaggon was unable to take advantage of a gilt-edged chance in the box. A shot from Jordan Cotterill flashed by the far post, while goalscorer Kinsella clipped the bar for Ferry on a rare counter-attack.
As time ticked away, Barry’s final chance was a Curtis McDonald shot headed off the line by Chris Evans, with the goalkeeper beaten. But it wasn’t to be Barry’s night.