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The victory means the Irish will face France in Sunday's final at the World League 2 tournament.
Wales will also make the final qualifiers in Johannesburg if they beat Scotland in the third place play-off.
Gareth Furlong put Wales ahead before Shane O'Donoghue, Ben Walker and Neal Glassey netted for the Irish.
Ireland, 10th in the world rankings, were strong favourites to account for the 34th-ranked Welsh but the visitors produced a strong challenge.
Furlong's early goal from a penalty corner left Wales ahead after the opening quarter but O'Donoghue and Walker struck in quick succession in the second quarter to give the hosts a half-time lead.
Wales had a couple of chances in the third quarter - including a missed penalty corner - before Glassey sealed Ireland's win by netting early in the final quarter.
France earned a 2-0 win over the Scots in Saturday's second semi-final.
Ireland's men guaranteed themselves a spot at the final World Cup qualifying tournament in the summer by beating Wales 3-1 at Stormont on Saturday.