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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.

Page, 20, has agreed a two-and-a-half-year contract at The Valley.
He made three first-team appearances for West Ham, all in the Europa League, and has previously been on loan at Coventry City and Cambridge United.
"He's quick, likes to get forward and is a good crosser. I really like that in a full-back," Charlton manager Karl Robinson told the club website.
"I got a chance to see him during his loan spell at Coventry and he's a left-back that fits in well with our system.
"We're building a squad here to get into that top six and Lewis will be an important part of what we are trying to do."
Find all the latest football transfers on our dedicated page.

Pinewood Group's two biggest shareholders have tentatively agreed to sell the famous film and television studios to a property investor.
The deal depends on Aermont, which runs property investment funds, securing financing in the next four weeks.
Pinewood's 007 stage is one of the world's largest and was used to film parts of Spectre and Skyfall.
Some of Star Wars: The Force Awakens was also filmed at Pinewood in Buckinghamshire. However, Harrison Ford, the actor who plays Han Solo, was injured when the door of the Millennium Falcon closed on him and broke his leg.
Goodweather Investment Management, which is owned by property investors Peel Holdings, and Warren James Holdings, owner of the eponymous jewellery chain, together control 65% of Pinewood Group and have agreed to the cash sale providing the buyer secures financing.
The prospective new owner intends to keep the existing management in place, led by chief executive Ivan Dunleavy.  The company has film and TV studios all over the world including in the US, Canada, Malaysia and the Dominican Republic.
Earlier this year, Pinewood Group retained investment bank Rothschild to examine its strategic options. In the past, it had been constrained from raising additional funding for investment via the stock exchange.
Shares in Pinewood were down 4.8% at 552.1p in afternoon trading.

Nicholas Woods, 41, and Tim Clark, 50, both of Lincoln Close, Erith, were also charged with false imprisonment and actual bodily harm.
They will appear in custody at Bromley Magistrates' Court on Monday.
Police found a second man at the scene with head injuries, who remains in hospital in a stable condition.
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.
[NEXT_CONCEPT]
League One club Charlton have signed left-back Lewis Page from West Ham for an undisclosed fee.
[NEXT_CONCEPT]
Pinewood film studios - home to the James Bond movies - are set to be sold for £323.3m.
[NEXT_CONCEPT]
Two men have been charged with murder after a 34-year-old man was stabbed to death in south-east London on Tuesday.