Gareth Thomas touches down for the Blues second try
Bristol (0) 0
Blues (14) 17
Tries: Molitika, Thomas
Con: Blair 2
Cardiff Blues secured their path through to the quarter-finals of the Heineken Cup with a well-earned victory over Bristol at the Memorial Ground.
But the Welsh region missed out on a home tie and instead have an away trip to Toulouse in the next round.
First-half tries from Maama Molitika and Gareth Thomas and a later Ben Blair penalty gave the Blues victory in difficult conditions in Bristol.
Both teams had tries disallowed early on but Bristol rarely threatened.
Martyn Williams was superb for the Blues and made a strong case for his inclusion in Wales' XV to face England in the opening game of the Six Nations championship.
And it was the veteran flanker who nearly opened the scoring for the visitors.
After Anthony Elliott had sliced his kick the Blues sniffed a chance to score their first points of the afternoon.
Eventually the ball found its way out to Williams on the wing and even though he touched down the television match official correctly ruled that Matt Salter had done enough and tackled the flanker into touch.
Earlier both sides had tries disallowed for forward passes and that was the closest Bristol came to scoring all game.
Eventually the breakthrough did come and it was Molitika who got it.
The normally reliable Bristol scrum failed to secure possession five yards out and flanker Molitika was on hand to collect the loose ball and cross from close range.
Former Wales captain Thomas got their second, diving over in the corner after a poor tackle from Sean Hohneck.
It was no more than the Blues deserved for a superb first-half performance in difficult conditions.
After the break Bristol continued to struggle with poor handling costing them on several occasions.
On the rare occasion the ball did find Tom Arscott on the wing the promising 20-year-old was often isolated despite looking threatening.
The Blues added to their lead with a Blair penalty with 25 minutes remaining and a third converted try would have secured a home tie in the next round.
In the dying minutes a penalty from Blues outside-half Nick Macleod failed to find the corner and with that chance went any hope of a third try.
The Blues' victory means Wales will have two Heineken Cup quarter-finalists for the first time since 2001.
Blues man-of-the-match Martyn Williams
"As a team performance it was brilliant, we've fallen at the last hurdle before and it is nice to go through.
"We played some nice stuff and we would have taken that before hand. We should have scored more but we're happy to go through
"We did find it difficult to get the ball off them and we knew the situation and that we had to score one more try but the conditions didn't allow us to put pressure on them."
Bristol: L. Arscott; T. Arscott, Higgitt, Brew, Elliott; Strange, O'Riordan; Clarke, Regan, Hobson, Winters, Hohneck, Salter, To'oala, Blowers.
Replacements: Linklater for Regan (54), Crompton for Hobson (60), Llewellyn for Hohneck (68), El Abd for Salter (68), Beveridge for O'Riordan (54), Hill for Strange (54), Cox for Brew (44).
Cardiff Blues: Blair; J. Roberts, Shanklin, G. Thomas, J. Robinson; Macleod, Spice; Jenkins, G. Williams, Filise, D. Jones, Tito, Molitika, M. Williams, Rush.
Replacements: G. Powell for Filise (71), Morgan for Tito (76), R. Thomas for M. Williams (80), Lewis for Rush (78).
Not Used: Rees, R. Jones, Selley.
Referee: Alain Rolland (Ireland).