The permutations for qualification were complicated but the Irish rendered them all academic with a ninth straight win over Scotland and a 17th successive test victory.
Fullback Hugo Keenan scored two tries and winger James Lowe, lock Iain Henderson, hooker Dan Sheehan and centre Garry Ringrose also crossed as Ireland controlled the match with accurate forward play and took their chances ruthlessly.
Ireland will return to the Stade de France next Saturday to face three-times champions New Zealand, while the Springboks take on hosts France in another blockbuster quarter-final in the same arena on Sunday. "We know this is where we want to be now, in the quarter-finals against the toughest opposition we can get," said Ireland skipper Johnny Sexton. "The way the draw was made three years ago, it turned out a bit unfair, but that's the hand that we were dealt, and we've got to be ready for that New Zealand next week." The Irish fans had again turned the French capital into a version of Dublin for the day and it took 63 seconds for the first full-throated roar from the sea of green in the stands.
Ringrose carved through the Scotland midfield from Ireland's first attack and offloaded to Mack Hansen, who sent his fellow winger Lowe over in the left corner.