A bonus point win keeps Neath in second place in the WRU Premiership.
Home tries came from hooker Josh Clark on his 50th appearance, prop Rhys Taylor on his first, full back Gareth Rees, centre Kieran Charles and an eighth of the season for winger Ki Morgan, outside-half Steff Williams converting four.
Met bagged two points themselves after tries by centre Gus Patterson, flanker Cerith Davies, prop Ollie Davies and replacement Tom Weekley, conversions were added by and Ross Mackay whose left-footed effort from the touchline on the final whistle earned the second point for the Met.