Cardiff RFC contested the first Heineken Cup final back in 1996 but, when it has come the knock-out stages since 2001, the Blues have been reduced to the role of spectators for the past six tournaments.
Wales centre Tom Shanklin, a Round 5 try scorer against 'Quins at a sodden Arms Park, has not yet tasted the excitement of the knock-out stages of the competition.
"It would mean a lot for the Blues to get through," said Shanklin. "The Blues have not qualified for the quarter-finals since I have been here - the last time Cardiff did that was in 2000 / 2001 - and, while we have had opportunities to qualify, none of those chances were quite as big or good as this.
"It really would be a great step forward for us if we can go through to the quarter-finals. However, it is going to be really tough. Bristol only narrowly lost by eight points over in Paris and they have been playing some good rugby this season.
"They will also be on their home turf this win over Harlequins has teed it right up for us - it is in our own hands.
"It is certainly a situation we would have settled for at the start of the tournament and, while we have had a few disappointing results recently, against 'Quins we were by far the better team and deserved to win.
"It was obvious we were never going to get a lot of tries in those sort of conditions but we controlled the game a lot better than we have done lately, we showed more composure and we kicked the points when it mattered.
"We have played a lot of rugby over the Christmas period but with a quarter-final of the Heineken Cup at stake we have to make sure we prepare correctly.
"I guess we can expect a pretty similar challenge from Bristol as they gave us in Round 1 - though a bit tougher and more stubborn at home - and they have a big pack and rush defence, but, weather permitting, hopefully there will be a bit more open rugby."
Paul Volley - a Heineken Cup winner with London Wasps in 2004 - believes the Pool 3 winners can go all the way to the showpiece occasion of the 13th Heineken Cup final at the Millennium Stadium on 24 May.The Harlequins captain has seen his own side's hopes of knock-out qualification ended but still feels the team which tops the group will be genuine title contenders.
"This Pool is wide open and it is going to be very close between the three teams - Bristol, Cardiff Blues and Stade Français - still in there," said the former England flanker.
"Obviously the match at the Memorial Ground is huge and, in all honesty, I cannot call it. Bristol will have home advantage, and the Memorial Ground is a hard environment, but the Cardiff boys are hugely committed and it is going to be a massive occasion and testimony to the Heineken Cup - you are playing the best in Europe and it is winner takes all.
"And why shouldn't the eventual winner come from this Pool?
"The Heineken Cup is all about getting through the Pool stages and qualifying for the knock-outs, that is the hardest part of the tournament.
"After that you are only two games away from the final and anything can happen."
Cardiff Blues Supporters' Club are running buses to the crucial match on Sunday 20th January, 3.00pm kick off. All Blues supporters are welcome! The buses leave the Arms Park at 12.30pm and leave Bristol at 7pm so should be back in Cardiff before 8.30pm.
It is a family friendly environment so book your places now and travel across the bridge with fellow Blues fans!
For bookings please call Clive on 07722 504180 or e-mail: firstname.lastname@example.org
Prices are - Adult members £10, Members concessions £7 and non members £15