A barnstorming performance from star man Gavin Ronan in the second row, two Andrew Claypole tries and some cool kicking from Ian Brooks was enough for victory.
Swansea wing Claypole opened the scoring with a mazy run down the wing, as the Whites went in 8-6 ahead at half-time, after both teams traded penalties in a turgid first half at St Helens.
The wing was at it again after the restart, extending the lead to 15-6 before two Swansea yellow cards – shown to Dai Watts and Rory Gallagher – stunted their second half progress.
Pooler took advantage with a try to storm back and lead 18-16, but outside-half Brooks held his nerve at the death with two late penalties.
The win moves Swansea closed to league leaders Merthyr, who were favourites to continue their lengthy winning streak at home to Beddau, but the weather intervened.
Bargoed’s clash with RGC 1404 was postponed due to a waterlogged pitch, as many Championship matches fell victim to the weather. Glynneath’s meeting with Newcastle Emily was postponed, as was Newbridge versus Cardiff Met, Llanharan against Bridgend Athletic and Narberth’s clash with Tata Steel.