The Bulls have to travel to Pontypridd, but will be full of confidence after they beat Division front-runners Bonymaen 26-22 at the weekend, courtesy of six goals from outside-half Rob Lloyd.
Team manager Justin Lewis said the hard-earned victory was perfect preparation for the trip to Sardis Road.
"We were 19-0 down after only 10 minutes, but we had chosen to play into the wind in the first half and that paid off," he said.
"It wasn't a day for the backs, so in the second half, we knew we had to keep it in the forwards and keep driving it up the middle. We've missed Rob Lloyd for the last three games, because he's a Marine and he's been away, and his kicking was crucial.
"We said before the game that we could win this one, and we knew it would give us a lot of confidence ahead of playing a Premiership side at Sardis Road.
"This season is strange - we can produce this sort of performance against the good sides, but can't seem to do it against the poorer sides."
In the other quarter-finals, Cardiff host Llandovery at the Arms Park, Maesteg take on Newport and Swansea welcome neighbours Neath to St Helen's.
Cardiff are staring Premiership relegation in the face, but will fancy their chances against the Drovers, who are only three points ahead on the table, having played one more game.
The two sides have met twice in the League this season, with results going to the home side. Cardiff won 21-13 in October, with Llandovery avenging that result with a thrilling come-from-behind 39-31 victory at the end of January.
Newport beat Maesteg 23-14 at Rodney Parade in October, but they will have to be on top of their game for the away trip this weekend.
Premiership table-toppers Neath will be favourites in their match against Swansea, having beaten the All Whites 17-6 in dire conditions last weekend. The last time Neath travelled to St Helens - in November - they came out on top 39-3.
The Half a Game initiative is currently sweeping across Wales and proving a major success. The scheme aims to give every young player at least half a game every weekend. WRU TV recently visited a festival in Narberth where clubs have fully embraced the initiative.
Both Bargoed and Swansea were seeking their first win of the Principality Premiership season this afternoon. It proved a fruitful day for the hosts - not only did they win, but Bargoed claimed a try bonus point.
Cardiff managed to keep their unbeaten record at home intact, but only just as Bridgend made them work extremely hard before the Blue and Blacks secured a hard fought Principality Premiership win at the BT Sport Arms Park last night.
Former Wales back row Andy Powell gives a guided tour of The Wern, home of Merthyr RFC, who are determined to prove a lot of people wrong and make their mark in their first season in the Principality Premiership.
Wales Sevens head coach Gareth Williams looks back on the Rio Sevens success where he helped GB win silver. He believes the successful campaign is a huge boost to his Welsh squad as they prepare for another World Series, as WRU TV's Graeme Gillespie discovers
British and Irish Lions head coach Warren Gatland will be heading back home to take on the All Blacks next year where for him, success for 2017 is all about going to New Zealand and winning a Test Series.
Last week all roads led to Eugene Cross Park where defending champions Ebbw Vale hosted this season's launch of the Principality Premiership. WRU TV's Graeme Gillespie was there to capture the thoughts of Damien Hudd, captain of Ebbw Vale, and WRU Head of Performance, Geraint John.
Llandovery made it three in a row when they defeated Aberavon in the final of the National Foster's 7s at BT Sport Cardiff Arms Park on Sunday. On another eventful day of sevens, Newport claimed the Plate and the Dragons won the women's crown
Last week saw Cardiff welcome players from around the world for the 21st Golden Oldies Festival. The tournament features players over 35 years of age, and this year's event saw a select few represent the WRU in a 'friendly' against the Wooden Spoon.
Wales Under 18 captain Callum Bradbury is delighted to have seen his side claim a narrow 18-17 victory against a strong SA Schools 'A' side to end the three-match Under 19 International Series in South Africa on a high note.