Prop David Pattison was the first player to annoy referee Phil Fear and he was yellow-carded for killing the ball, and flanker Nick Kelly soon followed him to the sideline for the same offence. Teams with 15 men haven't been able to beat Neath this season, and 13-man Newport had no chance as in-form young fly-half James Hook twisted the knife with four first-half goals.
Horgan broke from a scrum on the halfway line to set up a try for hard-working prop Cai Griffiths to give the home side a 30-6 lead early in the second half, and although the Black and Ambers began to apply the pressure, it was too little, too late. Replacement Neath scrum-half Martin Roberts scored his side's fourth and final try, with Newport finally crossing the opposition tryline through lock Darren Davies.
To add to the Neath players' celebrations, they walked off the field to news that nearest rivals Llanelli had crashed 27-23 at Aberavon.
In other games, Ebbw Vale winger Andrew Bevan bagged a pair of tries to complete a miserable weekend for Cardiff fans.
After the Blues butchered a 12-point lead against the Borders in the Celtic League on Friday night, the Cardiff Premiership side crashed 3-28 at Eugene Cross Park. Cross Keys ran in seven tries in a 41-15 training exercise against Llandovery and Caerphilly's woeful season continued with a 19-22 loss at Llanharan.
Fly-half Ross Watts was the toast of the Newbridge club after his six goals gave his side an 18-11 victory at Pontypridd to move further away from the bottom of the table.
Aberavon 27 Llanelli 23
Bedwas 34 Swansea 24
Bridgend 23 Pontypool 16
Cross Keys 41 Llandovery 15
Ebbw Vale 28 Cardiff 3
Llanharan 22 Caerphilly 19
Neath 37 Newport 13
Pontypridd 11 Newbridge 18