The result provisionally lifted the Serbians, who have not played on the big stage since the 2010 World Cup, to the top of their group with 11 points from five games.
Second-placed Ireland have 10 points from four games and can leap back into pole position if they beat third-placed Wales, who have six points from four matches, in the evening kick off.
Georgia thoroughly dominated the first half and missed several chances after Nika Kacharava gave them a sixth-minute lead with his first international goal after a howler by Aleksandar Kolarov.
The Manchester City defender, heavily criticised after recent performances for the Premier League club, gifted Kacharava a sitter with an awful back pass and the striker beat goalkeeper Vladimir Stojkovic with a crisp finish.
Valeri Qazaishvili missed a gilt-edged chance for the home side before Tadic equalised with a penalty on the stroke of halftime after a Georgian defender fouled winger Filip Kostic.
Stojkovic produced a triple save on the hour before Mitrovic fired Serbia ahead against the run of play.
The Newcastle United striker took Tadic's pass in his stride and rifled in a spectacular shot on the turn from 18 metres, silencing a vociferous home crowd in the Boris Paichadze Arena.
Tadic, who has scored four and assisted seven of Serbia's 12 goals in the campaign, was again instrumental as his deft touch released substitute and debutant Gacinovic to seal Serbia's win with his first international goal.
(Writing by Zoran Milosavljevic in Belgrade,; Editing by Pritha Sarkar)
