The visitors struggled to carve chances and Georgia stood firm to a succession of late crosses and corners.
Scotland suffered a 2-0 defeat on their previous visit to the Boris Paichadze Dinamo Arena which ultimately cost them a place at Euro 2008. And their latest loss, only Scotland's second of the campaign, could prove equally damaging as Group D rivals Poland, Germany and the Republic of Ireland all won here.
Georgia doubled their points tally, with their only other win coming across Gibraltar, and Scotland now might need something at home to world champions Germany on Monday night to maintain realistic hope of automatic qualification.
Gordon Strachan brought back Andy Robertson and Ikechi Anya after they were left out of Scotland's draw in Dublin. Charlie Mulgrew kept his place at centre-back in a familiar line-up. But the performance was out of keeping as Scotland lacked their normal tempo and creativity.
Georgia dropped unattached goalkeeper Giorgi Loria because he is lacking match practice but it was hard to tell if his replacement, Nukri Revishvili, was a capable replacement as Scotland failed to test him.
Scotland started on the front foot but they were almost caught out early on when a quick one-two took out Mulgrew on the halfway line and left the visitors wide open. But Kazaishvili opted to shoot from 30 yards out despite having two team-mates inside him and the ball trundled wide.
Gordon Strachan's side enjoyed superior possession and territory in the opening quarter but Georgia sat deep and made themselves difficult to break down. Steven Naismith and Shaun Maloney almost burst through and the former got in behind from Robertson's pass but his cutback was cleared.
Steven Fletcher was then just short of sliding in to meet Robertson's cross between the defence and goalkeeper.
But Georgia improved and had Scotland penned back before taking the lead. Scotland had plenty of men back as a straightforward high cross came in from the right, but neither Brown nor Mulgrew could get close enough to Kazaishvili as he took the ball down from Levan Mchedlidze's headed knockdown.
The Vitesse Arnhem player quickly lined up to shoot and drilled the ball low past David Marshall from 18 yards.
Mchedlidze, who scored against Scotland in 2007, forced a save from Marshall with a near-post shot following a short corner moments into the second half.
Maloney almost levelled direct from a corner on the 49th minute.
The Hull player's inswinger from the left was bouncing in with Revishvili scrambling to get there, but the ball hit Naismith on the line and spun over before the Everton forward was penalised for a foul on the goalkeeper.
That decision looked harsh but Naismith's claims that the ball was over the line were not backed up by television footage.
Fletcher soon hit the post from 18 yards following Maloney's forward pass but the offside flag was up.
Strachan made a double switch just before the hour mark when James Forrest came on for Naismith and Grant Hanley replaced Robertson. But it was Georgia who threatened next. Mchedlidze had a powerful 25-yard strike pushed over before hitting the side-netting on the break after James Morrison's misplaced pass.
Leigh Griffiths came on for Anya in the 75th minute but Scotland still struggled to carve out chances, with the hosts dealing comfortably with a number of crosses.
The visitors were given a chance to level in the 88th minute when Fletcher was fouled 22 yards out, but Maloney's free-kick hit a head in the Georgian wall and looped over, and their final opportunity passed them by in an increasingly desperate finale as Hanley headed wide from Mulgrew's corner.
Scott Brown defiant after defeat
Captain Scott Brown remained defiant after Scotland's Euro 2016 qualifying hopes were dealt a blow with a 1-0 defeat in Georgia.
The Scots went into the break trailing to a Valeri Kazaishvili goal and could not find a way back in the second half.
Gordon Strachan's side play world champions Germany at Hampden on Monday night which is where the Celtic skipper quickly turned his focus.
He told Sky Sports: "We didn't get the luck tonight to be perfectly honest.
"The group is still wide open, there are still nine points to play for.
"We can't feel sorry for ourselves, we have another big game on Monday night that we have to get ourselves ready for and go to try and get points there."
Brown added: "We need another good performance.
"It was an average performance tonight. We know we can do a lot better and hopefully that is on Monday.
"We had some nice inter-play and a couple of chances and another days that comes off but today it didn't.
"They shut up shop after they scored their goal.
"We have bounced back every single game. We have been one-nil down in most games and came back and we have won games from one down.
"It is all about bouncebackability and we have definitely got that in this changing room."
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