The tactical approach and brutish physicality produced by Joe Schmidt's men was too much for Wales to handle, as they fell to their first away defeat in the Six Nations since 2011.
Ireland struck for tries late on in both halves - flanker Chris Henry was on the end of a well-executed maul approaching half-time, while his Ulster colleague Paddy Jackson came off the bench to run in a satisfying 79th minute score.
Starting out-half Jonathan Sexton was hugely influential for the second week in a row, kicking astutely out of hand and landing five kicks from six attempts for a 14-point contribution.
Wales were 13-0 behind at the break and struggled to hang onto Ireland's coattails, with Leigh Halfpenny's 57th-minute penalty being their only score of this one-sided encounter.
Rhodri Jones did go close to grabbing a try in the rain-hit second period, but Ireland's dominant defence stood firm to make it 160 Championship minutes without conceding a try.
RBS 6 man-of-the-match Peter O'Mahony was in the thick of the action throughout, winning a number of turnovers at the breakdown and showing his versatility with a kick to touch and then a move into the second row after Dan Tuohy was forced off.
Collectively, Ireland were a notch or two above the men in red -quicker in both thought and deed - and they will relish the opportunity of travelling to Twickenham in two weeks' time for a shot at the Triple Crown.
Speaking after the game, Peter O'Mahony said: "At the end of the day we wanted it more than they did, that was evident by the end of it. I don't think the scoreline flattered us, but we fought for everything.
"That is where we need to be at, we need to be fighting for every 50-50 ball, everything that goes on the ground. They are the ones that make the difference.
"John (Plumtree) has put a big emphasis on our maul and our lineout, he wants us to be a great mauling and lineout team.
"You've guys there like Paul O'Connell, Devin Toner, Rory Best, Sean Cronin and Dan Tuohy - these guys spent an awesome amount of time on laptops and a savage amount of work.
"Credit has to go to all of them. John has put in great structures but the players are really driving that on."