A Jordan Follows double put Llanelli on the brink of a famous result in their Europa League second qualifying round first leg against Dinamo Tbilisi.
But the tie was left in the balance after the Georgians - who have appeared in the main stages of this competition or its predecessor, the UEFA Cup, on 11 occasions and are former Cup Winners' Cup finalists - scored a late away goal.
That came from the penalty spot, David Odikadze on target after Lloyd Grist fouled Irakli Lekvtadze, after Follows had struck in the eighth minute and again six minutes after half-time.
Another Welsh side, The New Saints, let a 1-0 lead slip as they went down 3-1 to Denmark's Midtjylland. Former Wales defender Steve Evans gave TNS a 59th-minute lead but it was quickly cancelled out by Rilwan Hassan.
Danny Olsen gave the Danes a first-leg lead (86) after Jude Nworuh was brought down in the penalty area by Evans' former Wrexham colleague Simon Spender, and substitute Mads Albaek added a third in injury time.
St Patrick's Athletic, from Ireland, grabbed an away goal but still trail Kazakhstan's Shakhter Karagandy 2-1. A rare goal from Nikola Vasiljevic gave Shakhter the lead, the former Bosnia and Herzegovina defender converting Zhambyl Kukeyev's corner.
And, after substitute Dave McMillan equalised for the Irish side, Vasiljevic amazingly popped up again to give his side a first-leg advantage.
Dead-ball specialist Dare Vrsic struck twice as another Irish side, Bohemians, went down 2-0 to Olimpija Ljubljana in Slovenia.
Vrsic notched from the penalty spot in first-half stoppage time after Ollie Cahill fouled Filip Valencic, and the midfielder curled home a free-kick after Liam Burns brought down Matic Fink.
Northern Ireland's Glentoran suffered a disappointing 2-0 home defeat to Ukraine's Vorskla Poltava. Serhiy Zakarliuka's corner led to an opener for Roman Bezus and Ahmed Januzi made it 2-0 before half-time.