Both sides started the game cautiously, with Ireland's Jordan O'Regan firing a free-kick low towards the Wales goal, but goalkeeper Andrew Wycherley getting down well to prevent the opening goal.
There was limited attacking threat in the first half, which Ireland dominated thanks to some strong midfield play from Patrick Crowley, who was one of the best of the home players on the night.
Conor Walsh produced the best chance of the half - after a smart one-two with Dean Swords, he unleashed a well struck side-footed effort which went narrowly wide of the goalkeeper's left hand post.
The second half was brighter from both teams, Wales especially, but not before Ireland let two half chances go to waste.
Wales made two changes after 65 minutes, one of which was to bring on midfielder Jamie Roberts, who orchestrated the majority of the Welsh attacking play in the last quarter of the game.
Mid-way through the second half, Roberts picked the ball up 35 yards from goal and unleashed a thunderous effort which rattled the bar after beating the goalkeeper.
With a quarter of an hour remaining Ireland's resistance was finally broken. A free-kick from the right hand side was sent curling towards goal and was headed home by defender Templeton from near the penalty spot.
Wales' well-disciplined defence was able to keep out the Irish onslaught for the final 10 minutes to secure a perhaps fortunate one goal victory. Ireland will now look to Wednesday's reverse fixture to gain some revenge on their neighbours.
REPUBLIC OF IRELAND: Craig Dunphy, Tony Archbold, Andrew McGovern, Troy O’Sullivan, Ryan Mawdsley, Conor Walsh, Lee Fetherston, Patrick Crowley, Jordan O'Regan, Dean Swords, Evan Coyne. Subs: Connal Flood for O'Regan 60 mins; Ciaran Kearney for Coyne 60; Michael Russell for Walsh 77; Fionn Curran for Fetherston 77.
WALES: Andrew Wycherley, Cai Owen, Jordan Pike, Ronan Templeton, Ben Nash, Sam Jones, Jack Rimmer, Ifan Jones, Nyasha Mwamuka, Tom Bibby, Lewis Evans. Subs: Tyler Brock for Evans 63; Jamie Roberts for Bibby 63; Tyler Aylward for Owen 71; Dan Dascalu for Pike 87.