Their anticipated last-eight clash in Wellington was confirmed after Wales secured Pool D runners-up spot by crushing Fiji 66-0 and Ireland swept past Italy to win Pool C.
The stage is now set for a first World Cup meeting between the countries since 1995, when Ireland's 24-23 success in Johannesburg booked a quarter-final place and sent Wales home early.
"We know each other inside out," said flanker and former Wales captain Jones. "We play against a lot of their guys week in, week out, just as they will know us. I imagine it is going to be a hell of a game.
"The stakes are higher as soon as you get into the knockout stages. You have to be clinical, and it is pleasing that we have been over recent weeks.
"We have taken the majority of our chances, which we possibly have been guilty of not doing in the past. We have to maintain that.
"We've got to make sure all the technical aspects of the game are tight. The lineout is going to be a massive encounter, and the breakdown has been ferocious in every game throughout the World Cup for every team, so we've got to make sure we dominate that as well.
"We are going to go about our business this week as we have done in the last four weeks."
Wales needed one point to guarantee a fourth quarter-final appearance in seven World Cups, and that was achieved courtesy of four tries during the opening 40 minutes.
Fiji had no answer to Wales' organisation, pace and attacking flair, with further impressive contributions from young guns like wing George North, centre Scott Williams and scrum-half Lloyd Williams, who all scored tries.
"We set ourselves a goal to get to the business end of things, and we've achieved that goal," Jones added. "But we are not getting too far ahead of ourselves. We've got over the first hurdle, as it were.
"The way the young players are scoring tries at the moment they must think international rugby is easy. There is a definite buzz about the camp, a lot of confidence there.
"I think there has been a certain maturity about the approach of everyone involved. We've focussed on the little things and I think it has paid dividends.
"Confidence is high. You take a lot of confidence by coming out of a pool like this one and reaching the quarter-finals.
"All the hard work is done now. It's about being physically fresh and mentally confident and ready for next weekend.
"Fiji were physical from the outset, as we knew they would be, but we came in with a game plan, a mindset and attitude. We stuck to it and it came off."
Whether or not Jones starts against Ireland could depend on the possible return to fitness of ankle injury victim Dan Lydiate, yet he believes competition for places is a significant squad strength.
"Selection is always subjective," he said. "All you can do is put yourself up for selection, give the selectors a headache and then you have to wait and see.
"That is the measure of this squad. Everyone is pushing and vying for a position, and everyone is worthy of wearing this jersey at this level. It has shown in the performances.
"That's the key to playing in a tournament like this. You need your 30 players, and they are all vitally important.
"It's nice to be here another week. The show goes on, as they say."
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