Scotland's two United Rugby Championship sides must overcome the odds to prevent favourites Leinster and Stormers reaching the semi-finals.
Leinster not only were losing European Champions Cup finalists but topped the URC table to secure a home tie against eighth-placed Glasgow Warriors.
Stormers are also at home to seventh-top Edinburgh after finishing second.
Mike Blair's side will take heart from the 20-20 draw the two sides fought out in the Scottish capital in October.
And, although it will be Edinburgh's first-ever game in Cape Town, they became the first Northern Hemisphere team to win in South Africa as part of the URC when they beat Sharks 21-6 in April.
They also won last time out, beating Glasgow 28-11 to leapfrog the visitors in the URC table, reclaim the inter-city 1872 Cup and secure qualification for next season's Champions Cup by topping the new Scottish-Italian mini-league within the parent competition.
However, John Dobson's Stormers have now won eight games on the bounce, culminating in a 26-21 win over Scarlets in Llanelli.
Leinster, meanwhile, will be smarting from Saturday's dramatic Euro final defeat in Marseille, when a late try meant La Rochelle lifted the trophy after a 24-21 victory, as they refocus in search of a fifth consecutive league title.
Whoever wins at RDS Stadium will secure a home semi-final against either Sharks or Bulls next weekend, while Glasgow and Stormers are vying to host either Ulster or Munster.
Team news
Leinster head coach Leo Cullen makes seven personnel changes, with captain and Ireland fly-half Johnny Sexton missing out with an ankle injury and being replaced with Ross Byrne, while James Lowe is rested and replaced with Rory O'Loughlin at left wing.
Ciaran Frawley starts at centre as Robbie Henshaw drops to the bench and, with Hugo Keenan rested, Jordan Larmour starts on the other wing as Jimmy O'Brien shifts to full-back.
Dan Sheehan starts in the front row, with prop Ronan Kelleher missing out through injury, and Joe McCarthy comes into the second row in place of Ross Molony. Meanwhile, Ryan Baird is in at six as Caelan Doris swaps to number eight, Jack Conan moves to the bench and Ireland lock James Ryan will captain the side.
Gregor Brown is named at openside flanker in only his second start for Glasgow, with Thomas Gordon dropping to the bench beside two Scotland internationals returning from injury - forward Fraser Brown and scrum-half George Horne.
Henry Pyrgos starts in place of the injured Ben Vellacott at scrum-half in the only alteration to the Edinburgh side that beat Glasgow.
Scrum-half Herschel Jantjies and centre Rikus Pretorius are handed starts in the only changes to the Stormers side that beat Scarlets to secure the South African Shield as the top finishers from their country in the URC table.
Jantjies comes in for the injured Stefan Ungerer, while Pretorius is at inside centre in place of Damian Willemse, who has been ruled out with an arm injury.
Utility back Sacha Mngomezulu is in line for a debut after being included among the replacements.
What they said
Leinster head coach Leo Cullen: "It's going to be a tough challenge. Glasgow are a good team, a niggly type of team as well, and we need to make sure we're in the right headspace for the game because it's a great challenge and hopefully we have a big crowd to cheer the guys on as well.
"You try your best to park the [La Rochelle] game, I think it'll be there in the back of our minds for the future, but it's onto the next challenge, isn't it?"
Glasgow Warriors head coach Danny Wilson: "Playing away at Leinster is as big a challenge as it gets. Leinster have been the benchmark in the league in recent years.
"We know we go into this game as underdogs, but we're confident that we have prepared well this week, welcome the challenge this game presents and look forward to putting our own imprint on the game."
Edinburgh head coach Mike Blair: "We're thankful to our backfield team who were able to able to get us out to Cape Town early, giving us the best possible chance to recover and prepare for Saturday's match by giving us a full week's training.
"As a squad, we really benefited from our two-week tour of South Africa back in April and its once again galvanised the guys - there's a great feeling of togetherness with this group. Stormers are a strong side and we know it's going to be a huge test away from home, but we have belief and confidence in the way we want to play."
Stormers head coach John Dobson: "A lot of hard work has gone into securing this home quarter-final, so we are determined to rise to the occasion.
"It has been a good week of preparation and everyone is excited about what should be a memorable day. We want to raise the intensity and make sure that we are at our best for the full 80 minutes, playing the kind of rugby that has got us into this position."
Team line-ups
Leinster: Jimmy O'Brien, Jordan Larmour, Garry Ringrose, Ciaran Frawley, Rory O'Loughlin, Ross Byrne, Jamison Gibson-Park, Andrew Porter, Dan Sheehan, Tadhg Furlong, Joe McCarthy, James Ryan, Ryan Baird, Josh van der Flier, Caelan Doris.
Keenan; J O'Brien, Ringrose, Henshaw, Lowe; Sexton (capt), Gibson-Park; Porter, Kelleher, Furlong, Molony, Ryan; Doris, Van der Flier, Conan.
Replacements: Sean Cronin, Cian Healy, Michael Ala'alatoa, Ross Molony, Jack Conan, Luke McGrath, Harry Byrne, Robbie Henshaw.
Glasgow Warriors: Ollie Smith, Josh McKay, Sione Tuipulotu, Sam Johnson, Rufus McLean, Ross Thompson, Ali Price, Jamie Bhatti, George Turner, Zander Fagerson, Rob Harley, Richie Gray, Ryan Wilson, Gregor Brown, Jack Dempsey.
Replacements: Fraser Brown, Oli Kebble, Simon Berghan, Lewis Bean, Kiran McDonald, Thomas Gordon, George Horne, Domingo Miotti.
Stormers: Warrick Gelant, Seabelo Senatla, Ruhan Nel, Rikus Pretorius, Leolin Zas, Manie Libbok, Herschel Jantjies, Steven Kitshoff, JJ Kotze, Frans Malherbe, Salmaan Moerat, Marvin Orie, Deon Fourie, Hacjivah Dayimani, Evan Roos.
Replacements: Andre-Hugo Venter, Brok Harris, Neethling Fouche, Adre Smith, Ernst van Rhyn, Nama Xaba, Godlen Masimla, Sacha Mngomezulu.
Edinburgh: Emiliano Boffelli, Darcy Graham, Mark Bennett, Chris Dean, Damien Hoyland, Blair Kinghorn, Henry Pyrgos, Pierre Schoeman, Dave Cherry, WP Nel, Jamie Hodgson, Grant Gilchrist, Luke Crosbie, Hamish Watson, Magnus Bradbury.
Replacements: Adam McBurney, Harrison Courtney, Lee-Roy Atalifo, Marshall Sykes, Ben Muncaster, Charlie Shiel, Jaco van der Walt, James Lang.