The Wellmen fell behind midway through the first half but were soon back on level terms following Jacob Wise’s header, his first in a Holywell shirt, to even the scores at the half time interval.
Despite chances in the second half, Town couldn’t get another goal and the visitors sealed the win with a second goal midway through the half.
Town next travel to Bangor on Saturday to take on CPD Bangor 1876, kick off 1.00pm