Wales will not be at next year’s World Cup in Russia after James McClean’s second-half goal sent the Republic of Ireland into the qualifying play-offs at the expense of Chris Coleman’s side.
The hosts dominated the game for large periods but fell behind to McClean’s powerful 57th-minute strike.
Hal Robson-Kanu had Wales’ best chance to score before that but his header was tipped over by Darren Randolph.
The win means the Republic finish second in Group D behind Serbia, with Wales in third. The draw for the play-offs will be held on 17 October in Switzerland.
Meanwhile, three-time runners up the Netherlands are all but out, Argentina is in trouble and Syria is in a play-off to keep their unlikely World Cup dream alive.
The tournament next year will consist of 32 teams, with hosts Russia joined by 31 qualifiers from around the globe.
The holders no longer qualify automatically, but Germany has progressed as group winners with a 100 per cent winning record in Group C.
There are 13 other sides guaranteed to be there: Brazil, Iran, Japan, Mexico, Costa Rica, Belgium, Saudi Arabia, South Korea, Spain, England, Nigeria, Poland and Egypt.
In Europe, the side that top each of the nine groups reaches the finals, while the best eight of nine runners-up go into November’s play-offs.