Leigh Halfpenny kicked three early penalties to put Wales into the lead, the third of which was a colossal effort from half way.
Halfpenny's boot then extended his side's advantage further after Samson Lee had been stretchered off the field, before Jonathan Sexton, who was winning his 50th cap for Ireland, pushed his first effort at goal wide of the posts.
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Sexton made amends with his second penalty, pulling Ireland back into contention in an intriguing first half that was low on try-scoring action but high on suspense.
The tide appeared to have turned in Ireland's favour when saw Sam Warburton was sin binned, but Wales managed their numerical deficit, holding onto the ball and probing the Irish defence before Dan Biggar boomed a drop goal between the posts shortly before the break.
Ireland came roaring out of the blocks at the start of the second half, and only some brave defensive play from the hosts kept their opponents out.
Bloodied and bruised but with their lead still in tact, Wales then began to push forward and scored the first try of the game when Scott Williams collected Biggar's pass and skipped beyond Tommy Bowe to touch down just after the hour mark.
Ireland came surging back, however, and Sexton's decision to kick for touch when faced with an easy three points was vindicated when Ireland were awarded a penalty try after Wales were penalised for collapsing the maul following the lineout.
Another Halfpenny penalty sent Wales a score clear on 74 minutes, but Ireland were given hope when Jonathan Davies was sent to the sin bin in the dying minutes.
However, Wales survived a late Irish onslaught to hold out for the win and keep alive their hopes of winning the Six Nations.