Saracens overcame a spirited Cardiff fightback to book a European Challenge Cup quarter-final date with Gloucester.
Max Malins was superb for Mark McCall's side, scoring a try and contributing two scores for Sean Maitland as Sarries pulled clear in the second half.
Dom Morris touched down the first try of the game for Sarries before Tomos Williams scored and created one for Owen Lane to lift Cardiff's hopes.
Rhys Carre burrowed in late on to set up a finish, but Saracens held out.
Three-time Champions Cup winners Saracens are in unfamiliar territory playing in Europe's second tier competition this season, but showed their intent to continue progressing with McCall restoring the likes of Maro Itoje and Malins to bolster their ranks.
However, they certainly did not have the game their own way against a Cardiff side struggling for form in the United Rugby Championship, belying those struggles with real grit and determination.
Their rhythm was upset throughout, and it took real class to break the Welsh club down, exemplified by Duncan Taylor's no-look pass for Morris' score and the subtle hands of Malins for both of Maitland's tries.
Owen Farrell also delivered a money-ball offload for Malins' score, as well as kicking 15 points.
Cardiff scrum-half Tomos Williams was a livewire during his stint, gliding between defenders for his try and again cutting through for Lane's effort, while Rhys Priestland's boot contributed 16 points to the tally from the tee.
But Dai Young's side will rue some of their missed opportunities, particularly when Lane failed to gather from Hallam Amos' surge, spilling with the line beckoning.
This exit ends any hope of reaching the Heineken Champions Cup, while Sarries' push for glory on all fronts remains.
Cardiff director of rugby Dai Young:
"It was a one-score game for most of the game and it was a game we could have won I feel. We left some points out there.
"I am really pleased with most of the stuff. We scrambled really well, our first-up defence was pretty good, our attack caused them problems and the set-piece held together.
"I am pleased with today but it leaves a little bit of frustration over where that's been the last two weeks really. Mark McCall said to me that's a game he thought we could have won."
The last-eight draw
Gloucester, winners in 2006 and 2015, join three other English sides, Wasps, London Irish and Sarries, in the last eight, along with two Scottish sides, Glasgow and Edinburgh, and two French sides, three-time former European champions Toulon and Lyon.
Edinburgh v Wasps
Lyon v Glasgow
Toulon v London Irish
Gloucester v Saracens
Ties to be played weekend of 6-8 May
Saracens: Goode; Maitland, Morris, Taylor, Malins; Farrell (capt), Davies; Barrington, Pifeleti, Carey, Itoje, Swinson, Christie, Earl, Wray.
Replacements: Lewis, Mawi, Wainwright, McFarland, B Vunipola, Van Zyl, M Vunipola, Segun.
Cardiff: Amos; Lane, Smith, Llewellyn, Summerhill; Priestland, Tomos Williams; Domachowski, Belcher, Lewis, Davies, Thornton, Lewis-Hughes, Navidi (capt), Botham.
Replacements: Dacey, Carre, Davies-King, Teddy Williams, Boyde, L Williams, Evans, Morgan.
Referee: Pierre Brousset (Fra).
Assistant referees: Luc Ramos & Flavien Hourquet.
TMO: Eric Gauzins.