Tom Lawrence lashed home right-footed from just outside the area in the 49th minute to earn Wales only their fourth victory in nine qualifying games and put them clear in second spot in Group D with 17 points, a point behind leaders Serbia who suffered a shock 3-2 loss at fourth-placed Austria.
Serbia are still favourites to win the group with a final home game against Georgia on Monday, while Wales play third-placed Ireland in what looks like becoming a shoot-out to see who finishes as runners-up to claim a probable playoff spot.
Ireland, who beat Moldova 2-0 on Friday, have 16 points.
Wales, bidding to reach the World Cup finals for the first time since 1958, would be guaranteed at least runners-up spot in the group providing they avoid defeat against Ireland.
However victory for either side would see them top the group if Serbia lost their final game.
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