The winners, from Division 5 South West, claimed tries by locks Scott Davies and Matthew Owen with outside half Tom Blizzard converting one and adding four, crucial penalty kicks.
The upper Swansea Valley side who are second in their division, will be entering new territory in the fourth round as they have never reached this stage of the competition in previous seasons.
Four North Wales sides will be in the draw after Menai Bridge, Shotton Steel, Mold and Llandudno all survived the third round. Division 3 North side Menai Bridge upset the form book by travelling to Wrexham of Division 2 North and recording a 19-12 victory, but Welshpool were unable to join the giant-killers after being soundly beaten 64-7 at Shotton Steel
Llangefni were favourites to defeat visitors Mold, having already recorded a Division 2 North league victory over their opponents, but Cup matches are different and Mold edged home 10-7 to go through to round four.
Llandudno had defeated Colwyn Bay 29-0 at home in the league this season but they were drawn to play at Colwyn Bay’s Brookfield Drive ground. It made little difference as Llandudno won 17-0.
Last year’s beaten finalists Fishguard of Division 4 West will not be going to the Millennium Stadium this season. They travelled to Tregaron of Division 6 West and were beaten 11-10 on the School Field.
Bettws of Divison 5 South East and Tredegar Ironsides of Division 6 East drew 17-17 at Ty Coed Fields but it is the Ironsides who go through after winning the try count 3-2.
Canton, who are enjoying one of their best seasons and lead Division 5 South East, suffered their heaviest defeat in years when they travelled to Glyncoch and were soundly thrashed 95-0. The Cardiff-based side’s task was made all the harder after injuries and unavailability led to only the bare minimum of players travelling, and they were no match for the Division 4 South East club who have only lost twice in the league to date this season.
