The Nomads were soon under the cosh at Llandarcy Park as Neath left back Jack Jenkins put the home side in front with a wonder strike from 30 yards in the third minute.
It soon got worse for the Nomads when defender Allan Glover was dismissed after 19 minutes for an elbow on Eagles' striker Andrew Hill and the 10 men were always chasing the game after that.
Hill provided the opening for Matthew Rees to double the lead on 35 minutes with a 12-yarder past visiting keeper Paul Pritchard and only a last-ditch clearance from Chris Melia then denied Dale Evans.
But Quay managed to keep out the hosts until the final five minutes when a Lee Bevan header and an eighth league goal of the campaign for Hill completed an impressive win that takes Andrew Dyer's men into Christmas in the top half of the table.
Stats and report courtesy of welsh-premier.com