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.
Ahead of their SSE SWALEC Bowl Final clash with Taffs Well at Principality Stadium on Sunday, Burry Port share their #FABXV nomination with WRUTV in the search for Welsh rugby's greatest volunteers. Everyone can get involved by sending nominations via twitter to @WRU_Community using the hashtag #FABXV
Cardiff Blues prop Gethin Jenkins and Ospreys centre Ben John look ahead to the first game at Principality Stadium in Saturday's double header which is promising to be a special occasion for all Welsh fans.
Carmarthen Quins Director of Rugby Ian Jones and committee member Jeff Thomas along with Llandovery chairman Handel Davies look ahead to Sunday's SSE SWALEC Cup showdown where both teams are out to prove 'West is best'
SWALEC ambassador Shane WIlliams is looking forward to Sunday's Finals Day where the Cup, Bowl and Plate offers a great opportunity for players and teams to experience the magic of playing at Principality Stadium
Carmarthen Quins coach Richard Kelly believes it is an exciting time to be part of the Scarlets region as his side take on local rivals Llandovery in the SSE Swalec Cup final on Sunday, as WRU TV's Graeme Gillespie discovers
Scarlets long serving prop Phil John talks to WRU TV's Graeme Gillespie about Judgement Day IV and SSE Swalec Cup finals day. The last time Llandovery were in the cup final in 2007, the Drovers claimed the spoils with Phil playing a major role in the engine room.
Meet Aberdare coach Luke Thomas whose #FABXV nomination goes to super volunteer Daz with a whopping 10 things he does for the club each week, all except the ironing! You can also join in the search for Welsh rugby's greatest volunteers, by sending your nomination via twitter to @WRU_Community using the hashtag #FABXV
SSE Swalec Cup kings Pontypridd travelled to Swansea, fully expecting a return to their second home but Llandovery had other ideas as they also sought victory in the semi-final to earn the right to play the final at Principality Stadium