But the men in green are counting the cost of the win after Munster's Peter O'Mahony has been ruled out of the rest of the tournament with knee ligament damage, captain Paul O'Connell is expected to follow suit after suffering a hamstring issue and talismanic Leinster fly-half Jonathan Sexton was also carted off with an injured groin.
Leading 9-6 heading into the interval at the Millennium Stadium, Rob Kearney - who scored two GUINNESS PRO12 tries for Leinster last term - dotted down to increase the lead before Munster scrum-half Conor Murray added a further late try.
That win sets up a mouth-watering quarter-final with Argentina, who have former Cardiff Blues full-back Joaquin Tuculet in their ranks, in Cardiff next Sunday.
Scotland are also through to the last eight after a thrilling 36-33 win over Samoa on Saturday - Glasgow Warriors winger Tommy Seymour notching one of their three tries.
Captain Greig Laidlaw scored what proved to be the decisive try in the final seven minutes although the Scots had to cling on after Motu Matu'u's late score.
Cardiff Blues new boy Rey Lee-Lo scored another of Samoa's four tries while Benetton Treviso's Filo Paulo also started but Scotland did just enough to book a quarter-final clash with Australia next weekend.
The Wallabies topped Pool A as they edged past Wales 15-6 on Saturday although both sides had already qualified for the quarter-finals.
Ospreys' Dan Biggar kicked all six of Wales' points but the big news for Warren Gatland's men was Scarlets star Liam Williams being ruled out for the rest of the World Cup with a foot injury.
As they prepare for a quarter-final with South Africa, who have GUINNESS PRO12 duo Ruan Pienaar and Zane Kirchner in the squad, Williams' absence is just the latest selection headache for Gatland.
Treviso duo Edoardo Gori and Alessandro Zanni notched a try apiece as Italy ended their tournament on a high by beating Romania 32-22, ensuring qualification for the 2019 Rugby World Cup, while Glasgow Warriors lock Leone Nakarawa dotted down for Fiji in their 47-15 triumph over Uruguay last Tuesday.
And there was a distinct GUINNESS PRO12 flavour to Canada's narrow 17-15 loss to Romania on the same day as the Canucks' two tries were scored by Ospreys winger Jeff Hassler and Scarlets flyer DTH van der Merwe - the latter dotting down for the fourth time at this World Cup.
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