The Port Talbot side took an early lead against Barry from the penalty spot, Liam McCreesh scoring, but were unable to defend against the Barry attack in a weather-affected game, with high winds coming off the sea.
Barry had already equalised when McLaggon scored after half an hour, but bossed the second half.
Intricate work by Fahiya and McLaggon outside the box set up Callum Sainty to fire home after 54 minutes, while Barry’s third came when a shot from outside the box was deflected into his own net by Lido defender, Jackson Hall.
Barry’s fourth goal came from a corner. Kayne McLaggon had failed to get the ball over the line in a goalmouth melee, but was on hand to score direct from the resulting corner.