David Siradze's injury-time strike spared Georgia from embarrassment against a limited but stubborn Malta side in Tbilisi.
Georgia's last competitive home win came three years ago, when they beat Scotland 2-0, and a strong showing from visiting keeper Justin Haber almost denied them again tonight.
Malta could even have snatched a win themselves through Andre Schembri 10 minutes from time, but they were beaten at the last when substitute Siradze headed home.
That was harsh on Haber, who made an impressive save from Gogita Gogua from the only clear-cut chance of the first half.
Malta defender Jonathan Caruana headed over at the other end, while Georgia's Zurab Khizanishvili collected a yellow card which rules him out of the next qualifier against Latvia.
Home coach Temuri Ketsbaia replaced strikers Giorgi Merebashvili and Vladimir Dvalishvili with Siradze and Aleksandr Iashvili at the break and his side looked more lively, but Gogua missed an open goal shortly afterwards.
The same player was denied by Haber before Malta's golden chance arrived. Schembri was left one-on-one with Nukri Revishvili, but the keeper saved with his feet and the chance was gone.
Siradze could not connect with Malkhaz Asatiani's pass after the full-back dribbled through the Malta defence - but he was on the spot in the 91st minute to seal the win which takes Georgia to five points after three games in Group F. Malta remain bottom and pointless.