The Hearts forward came off the bench to find the back of the net after Giorgi Chanturia opened the scoring in the first half.
The draw kept the Scots level with the Georgians on seven points, with Holland and Slovakia out in front in Group Three on 10 points.
Dundee United youngster Ryan Gauld was handed his Under-21s debut from the start, as Billy Stark made three changes from the last match.
The 17-year-old had earned his first call-up to the squad thanks to impressive club form and was drafted straight into the side.
Andrew Robertson and Lewis Macleod - who netted in the 2-1 defeat in Tbilisi last month - were also added to the starting line-up for the clash in Paisley.
The young Scots were keen to make amends for their last outing and dominated the opening spell in this match.
A Callum McGregor corner picked out Stevie May in front of goal but the in-form St Johnstone forward was unable to keep his header down and on target.
Stuart Armstrong's cross was then met by the head of Jordan McGhee who nodded wide of the upright as the home side pressed for the opener.
Chances were limited early on for Georgia but they gradually began to impose themselves on the game and Chanturia tested Jordan Archer with a well-struck shot that the goalkeeper managed to gather.
The visitors then claimed for a penalty when Jambuli Jigauri went to ground just inside the box but no spot-kick award was forthcoming.
The Georgians were ahead a couple of minutes later anyway when Chanturia cracked a shot in off the post and over the line on 31 minutes.
Scotland tried to haul themselves back into the game after the restart and Macleod tried his luck with an audacious low drive from distance that he drilled wide.
The home side were forced to make a change after 57 minutes when Dylan McGeouch limped out of the action following a crunching tackle in the middle of the park and was replaced by Kenny McLean.
Georgia looked more than capable of adding to their earlier goal and Lasha Parunashvili passed up a decent chance when he failed to keep his shot on target from close range.
Paterson was thrown into the action with 20 minutes to go, with McGregor making way for the Hearts man.
Scotland continued to search for the leveller and Gauld dragged a long-range effort wide, before May saw his own shot clawed to safety by goalkeeper Giorgi Nadiradze.
Hopes of a comeback were almost shattered by Jano Ananidze's ferocious strike but Archer did well to push past the upright.
The Scots were back on level terms moments later when Paterson met McLean's free-kick with an overhead kick after 84 minutes to make it 1-1.
The draw saw Stark's men drop points at home for the first time in the campaign but at least keep themselves in the hunt for a play-off spot.