Chasetown had the first attempt at goal in an even opening 20 minutes. Will Whieldon tried his luck from long range and Bay keeper Paddy Rutter had to adjust quickly to kick the ball away.
The hosts went close again following neat build up play between Whieldon and Tom Hill but the striker failed to trouble Rutter.
Chasetown deservedly took the lead 5 minutes before half time. Academy star Liam Kirton received the ball inside the box and, on the turn, fired into the top corner of the net.
Kirton deservedly made it 2-0 in the 70th minute. He received the ball on the edge of the box and drilled a low shot beyond the reach of Rutter.
The hosts stretched their lead with a clinical third goal. Whieldon broke into the box and chipped up to the far post where Tom Hill headed home unmarked.