Gareth Bale scored his 25th goal for Wales but Georgia fought back strongly to earn a deserved 1-1 draw in a World Cup Group D qualifier in Cardiff on Sunday.
It left Wales, surprise semi-finalists at Euro 2016, with five points from three games and at risk of losing the group leadership after the day's later matches.
Georgia took their first point, following narrow defeats by Austria and Ireland.
Wales, who have only ever qualified for the finals once, in 1958, took the lead in the 10th minute when Real Madrid's Bale leapt above his markers to head in Joe Ledley's corner.
He is now only three goals behind Ian Rush's national record of 28 goals.
The home team paid for a lack of urgency, however, after 57 minutes when Tornike Okriashvili headed an equaliser.
Georgia, dangerous on the counter-attack, could have gone on to win but Levan Mchedlidze missed when clean through and Valeri Qazaishvili hit the bar.
The other Group D matches, in which second-placed Serbia meet Austria, and bottom team Moldova play Ireland, were taking place later on Sunday.
Next month Wales are at home again, to Serbia, while Georgia play Moldova.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)