Tom Lawrence’s thunderous second-half strike against Georgia kept Wales’ hopes of automatic World Cup qualification alive and in turn boosted their prospects of reaching the play-offs.
Wales are second in Group D, one point behind leaders Serbia and one ahead of third-placed Republic of Ireland with one game to play.
Chris Coleman’s side will qualify automatically for next summer’s tournament in Russia if they beat the Republic in Cardiff on Monday and Serbia fail to overcome Georgia.
Wales will finish at least second if they avoid defeat against Martin O’Neill’s side, a scenario which would leave them in contention for a play-off place.
The eight best second-placed teams from the nine groups enter the play-offs, and this victory puts Wales fifth in those rankings.
Victory in Tbilisi – the first time Wales have beaten Georgia – sets the stage for the Republic match, which is likely to be the most intense Wales international staged at the Cardiff City Stadium.