Ponty were far too strong for Championship side Tata Steel, winning 43-6, and the 2011 Cup winners will be confident of making further progress when they travel to Eugene Cross Park.
Ebbw Vale will be joined in the quarter-finals by two other Championship sides after a Lee Meads try and a penalty try helped Bargoed to a 17-13 win over Bridgend and Blackwood saw off fellow-Championship opposition, Glamorgan Wanderers, with a four-try salvo in a 32-18 success.
Bargoed face a difficult trip to six-times winners Neath, while Blackwood host Carmarthen Quins who were the 2010 finalists.
The Welsh All Blacks defeated holders Cross Keys 19-12 to reach the quarter-final stage but Keys put on a remarkable performance after being reduced to 14 men for most of the second half.
Two late penalties from full back Jack Maynard won the day for Carmarthen Quins who edged out Bedwas 23-21 to reach the quarter-final.
The final tie will be between three-times winners Swansea and Aberavon who were finalists way back in 1974 and 1975 but have yet to lift the trophy.
Swansea knocked Newport out of the cup at Rodney Parade, winning 17-14 thanks to a last minute penalty goal from Cameron Clement, while Aberavon touched down five times in beating Beddau 44-6.
SWALEC Cup quarter-finals, to be played the weekend of 23 March
Blackwood v Carmarthen Quins
Ebbw Vale v Pontypridd
Neath v Bargoed
Swansea v Aberavon
Heol y Cyw booked their place in the quarter-finals after defeating defending champions Penallta 25-3. The SWALEC One East side crossed three times with Mike Huckridge adding the remaining points with the boot.
They have been rewarded with another home tie when they entertain Two East's Pill Harriers.
Pill edged through on try count after drawing 24-24 at Taibach but now find themselves drawn away from home for the fourth successive tie.
Ystrad Rhondda are favourites for the Plate following their early season form in One East which they lead with only one defeat to date. They beat Treorchy 30-18 in a re-arranged third round tie and now meet Kenfig Hill to decide who hosts Felinfoel in the quarter-finals.
'Foel knocked out North Wales side Pwllheli 28-18 to move into the last eight. Five penalties from Josh Jones sent Rhydyfelin through in extra time of their fourth round tie at home to Loughor. The sides were level at 12-12 until Jones landed his fifth kick in the second half of extra time.
They will travel to the winners of the Waunarlwydd / Llantrisant tie.
Cwmllynfell beat Builth Wells 37-15 in round four but will travel in the quarter-finals. They will play at the home of the winners of the Kidwelly / Garndiffaith fourth round match.
SWALEC Plate quarter-finals, to be played the weekend of 23 March
Kidwelly/Garndiffaith v Cwmllynfell
Ystrad Rhondda / Kenfig Hill v Felinfoel
Waunarlwydd / Llantrisant v Rhydyfelin
Heol y Cyw v Pill Harriers
In one of the shocks of the day, Cambrian Welfare of SWALEC Division Six knocked holders Glyncoch out after an 18-15 victory to reach the quarter-finals.
Tries from Zack James and James Wicks and eight points from the boot of Julian Huntley were enough to dump the holders and Welfare will now travel to the winners of the Cilfynydd / Bettws tie.
Penlan put paid to the students of Cardiff Medicals 21-7 with tries from Jason Garmey, Rob Green and Robert Di Lulio. They travel once again in the quarter-final to play the winners of Blaenavon / Glyncorrwg.
Pontycymmer have been drawn to visit the winners of Fishguard / Shotton Steel after they went through with a narrow 9-5 success at Penybanc.
The final tie will see Nantyglo, 39-21 victors over Denbigh, travel to the winners of the Wattstown / Tycroes fourth round tie.
SWALEC Bowl quarter-finals, to be played the weekend of 23 March
Fishguard / Shotton Steel v Pontycymmer
Blaenavon / Glyncorrwg v Penlan
Cilfynydd v Bettws / Cambrian Welfare
Wattstown / Tycroes v Nantyglo