A Jordan Follows double gave Llanelli a notable scalp against Dinamo Tblisi in the second qualifying round of the Europa League.
Follows opened the scoring on 8 minutes when he slotted past the goalkeeper from Antonio Corbisiero's ball over the top of the static Dinamo defence.
The striker doubled the lead with a beautiful left-foot curler which found the top corner on 51 minutes.
But Dinamo grabbed an away goal when David Odikadze scored a late penalty.
Craig Williams almost restored Llanelli's two-goal advantage in the final seconds of added time, but Dinamo goalkeeper Giogi Loria stretched every sinew to get his finger tips to his lop and push the ball wide.
Llanelli were without five senior players for the first leg at Parc y Scarlets due to suspension, including top scorer Rhys Griffiths.
But the Welsh Cup winners were certainly not out-classed by their more illustrious opponents, who won the Uefa Cup Winners' Cup in 1981.
Dinamo were limited to long-range shots as they tried to reply to Follows' well-taken double, but Lloyd Grist's clumsy challenge nine minutes from time on substitute Irakli Lekvtadze gave the visitors what could prove to be a crucial away goal.
Despite the late setback, Llanelli manager Andy Legg described his side's performances as one of the best ever seen by a Welsh Premier side in Europe.
"To beat a club with the stature of Dinamo Tblisi is an outstanding achievement," said the former Wales defender.
"I'm really chuffed for the lads and it doesn't really mater what happens in the second leg - they can go out there and hold their head up high and give it their best shot.
"They've got nothing to lose."
Llanelli: Morris, Chris Thomas (Legg 67), Stuart Jones, Surman, Bowen, Corbisiero, Follows (Ross Jones 72), Ashley Evans, Williams, Grist (Batley 89), Bond.Subs Not Used: Richards, Stephen Jenkins, Orme, Secker.
Booked: Corbisiero, Follows, Surman, Grist.
Goals: Follows 8, 51.
Dinamo Tbilisi: Loria, Homola, Jigauri (Tekturmanidze 65), Koshkadze, Kakhelishvili (Yague 70),Odikadze, Coto (Lekvtadze 54), Rekhviashvili, Kakubava, Xisco, Kvekveskiri.Subs Not Used: Nadiradze, Tomashvili, Pirtskhalava, Pantskhava.
Booked: Kakhelishvili, Lekvtadze.
Goals: Odikadze 81 pen.
Ref: Mattias Gestranius (Finland).