Seamus Coleman scored the only goal of the game as the hosts kept up their 100% record against Georgia to move onto four points from two games in Group D.
Ireland boss Martin O'Neill opted to start James McCarthy despite the Everton player having been sidelined for more than a month with a groin injury, but it was Jonathan Walters who was the first to threaten for the home side.
Coleman raced down the flank and delivered an inviting ball into the middle that Walters nodded back across goal, but Giorgi Loria in the Georgia goal did just about enough to deal with the danger.
The visitors didn't have to wait much longer for their opening chance as they went in search of a first ever victory against Ireland, with Valeri Kazaishvili flashing a shot just past the post having turned away from his man inside the box.
If that wasn't enough of a warning shot for Ireland, the hosts found themselves very lucky to still be level with less than 10 minutes remaining of the first half when Georgia hit the crossbar and then the post in quick succession.
The home side began making up for their lacklustre first-half display after the interval, and it took just 10 minutes for them to break the deadlock when Coleman bundled through a number of challenges before scrambling the ball home for his first ever international goal.
Ireland had the ball in the back of the net once again just three minutes later, but on this occasion James McClean's header was correctly ruled out for offside.
Georgia had only scored once in their four previous visits to Ireland, and they showed few signs of improving that record in the second half as Ireland edged closer to the victory.
Indeed, the hosts were inches away from sealing the win once and for all in stoppage time when McClean met a cross from Walters but saw his header crash off the crossbar.
The miss did not prove to be costly, though, as Ireland held out through a lengthy stoppage time caused by an injury to Robbie Brady to pick up their first victory of the qualifying campaign.
The win takes Ireland joint top of Group D alongside Wales, Austria and Serbia, all of whom have four points from their opening two games.