It was Wales' first Six Nations defeat since Ireland beat them two years ago, while they have not won in the tournament on Irish soil for eight years.
Tries by full-back Jordan Larmour, prop Tadhg Furlong, flanker Josh Van Der Flier and wing Andrew Conway saw Ireland home as they moved impressively towards a Twickenham appointment with England on February 22.
Andy Farrell's team also remain on course for a Grand Slam, but Wales' hopes of a clean sweep are over, and they could have few complaints.
Ireland captain Johnny Sexton converted two of Ireland's tries, with Wales fly-half Dan Biggar adding the extras to a sharp Tomos Williams score and Leigh Halfpenny converting flanker Justin Tipuric's touchdown in added time.
There was no doubting Ireland's supremacy as they improved considerably on last weekend's performance in beating Scotland.
Wales, though, have plenty of questions to answer during the build-up to their next game against a resurgent French team in Cardiff following Wayne Pivac's first defeat as head coach.
Ireland showed two changes from the side that beat Scotland, with centre Robbie Henshaw replacing an injured Garry Ringrose and flanker Peter O'Mahony also starting in a reshaped back-row that saw CJ Stander move to number eight instead of Caelan Doris.
Wales were under immediate pressure after Ireland wing Jacob Stockdale's kick left them retreating, but a strong early scrum reaped a penalty that was cleared to touch.
The Wales forwards enjoyed early supremacy, proving technically efficient, and Ireland did not gain their first penalty until the 13th minute as both sides went about their business like two sparring boxers.
Ireland had more than a fair share of territorial control, yet just as a tight opening quarter appeared to be moving towards a scoreless conclusion, the home side struck.
They initially kept possession tight in the forwards, and when it was eventually moved wide, Larmour finished impressively after brushing off a Tompkins challenge.
Sexton made a hash of the conversion attempt, but Ireland were off and running, leading 5-0 after finding their feet in what was proving an attritional encounter.
It came just at a time when Wales needed to find an attacking spark, but their response was impressive as Biggar darted inside and outside of Irish defenders before sending a scoring pass to Williams.
Biggar's conversion made it 7-5, but Williams went from hero to villain just five minutes later.
Wales skipper Alun Wyn Jones won lineout ball deep inside his own 22, throwing the ball to Williams, but he dropped it and Ireland gained an attacking scrum from which they scored when Furlong crashed over.
Sexton converted to restore a five-point advantage, before Ireland closed out the half and trooped off holding a 12-7 lead.
Wales could not get going early in the second period, and Ireland hit them with a third try after 47 minutes when Van Der Flier claimed a close-range touchdown that Sexton converted.
Wales thought they had cut the deficit 10 minutes later after Hadleigh Parkes went over, but video replays showed he lost control of the ball as he attempted a one-handed touchdown under pressure, and Ireland escaped.
It was a key scoreboard moment, and Wales did not gain another opportunity until Tipuric stretched over in the dying seconds as Ireland comfortably closed out the contest with Conway's 76th-minute try, and they will now march confidently on to Twickenham.