The Division One North outfit raced into a 24-0 halftime lead with tries from centre partners Airon Jones and Emrys Evans, and a third from flanker Eryl Jones, to virtually put the game beyond the reach of the home side.
But Dunvant recovered after the break, recording three tries of their own through full back Adam Williams, centre Danny Davies and scrum half James Richards to make It a major fight. But two more penalties from Nant full back Carwyn ap Myrddin were enough to see the North Walian side through.
Joining Nant Conwy in the last eight will be fellow northerners Bethesda, who comfortably saw off the threat of visiting Nelson, running in six tries in a 40-3 win. No 8 Dylan Thomas notched a brace of tries as his side ran in three in each half. There were also touchdowns from scrum half Graham Davies, centre Ben Stelmazek, outside half Matthew Parry and fullback Llion Lloyd.
Andrew Hutchins and Dai Gratton ran in the tries for Ystrad Rhondda as they secured an impressive 12-10 away win at Crymych. Alex Webber added a conversion in what proved to be a tight and low-scoring encounter at Parc Lloyd Thomas.
Builth Wells and Pontypool United - who both recorded away wins at Abertillery Blaenau Gwent 23-13 and Skewen respectively - also advanced to the next round of the Plate.
Meanwhile, the fixtures between Cwmllynfell and Glynneath, Maesteg Quins and Kidwelly as well as Senghenydd and Penallta were all postponed after falling foul to the weather.
In the SWALEC Bowl there were five away wins from the seven matches that survived the weather as Caerleon, Talywain, Tycroes, Glyncoch and New Tredegar all matched into the quarter-finals. There were also home wins for Amman United and Dolgellau.
New tedegar's 11-10 triumph at Hafodyrynys ended a run of 11 straight wins for the home side and was only their second defeat of the season - and their first at home for the Division 5 East outfit.
SWALEC PLATE ROUND 4
Abertillery B G 13 23 Builth Wells
Bethesda 40 3 Nelson
Crymych 10 12 Ystrad Rhondda
Skewen 22 26 Pontypool United
Cwmllynfell P P Glynneath
Maesteg Quins P P Kidwelly
Senghenydd P P Penallta
SWALEC BOWL ROUND 5
Amman United 28 0 Gowerton
Barry 5 27 Caerleon
Cardiff Quins 18 25 Talywain
COBRA 14 22 Tycroes
Dolgellau 25 22 Milford Haven
Glyncorrwg 9 13 Glyncoch
Hafodyrynys 10 11 New Tredegar
Resolven P P Treherbert