Bay became the weekend’s ninth North Wales qualifier for the last 16 with a deserved victory at Cymru South hosts Carmarthen.
The Seagulls were in the ascendency from the start, Jordan Davies’ early on-target strike deflected behind for a goal-kick off his team-mate Issa Kargbo.
It was no surprise when the Cymru Premier visitors took a seventh-minute lead.
A free kick from wide left was curled brilliantly into the net via the post by Davies, who celebrated his ninth goal of the season.
Trystan Jones’ corners from the left were a major weapon for the Old Gold, and one such delivery was so nearly flicked home from point-blank range by Morgan Weaver.
Bay went 2-0 up in the 22nd minute when a cross from the right was headed goalwards by Williams and hit team-mate Lewis Sirrell, who turned and was able to force the ball into the net.
Another Jones corner was a fraction away from getting the touch needed to make it 2-1 at the interval.
Mike Wilde’s men were three-up midway through the second half when Matty Hill crossed low from the right, Sirrell’s back-heel reached Sol Forde whose effort was fumbled by Idzi and Louis Robles converted the loose ball.
Carmarthen hit back in the 80th minute when Thomas Dyson’s ball in from the left was superbly headed home by veteran striker Liam Thomas, but it was too little, too late for the home side.
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