Keane, Richard Keogh and Simon Cox were all on target for Giovanni Trapattoni's side, who were some distance below the performance they produced in Wednesday's draw with England at Wembley.
Keane equalled Given's all-time appearance tally for Ireland when he was introduced at the interval as Ireland warmed up for Friday's World Cup qualifier with the Faroe Islands with a comfortable victory over limited opponents who saw goalkeeper Giorgi Loria dismissed in the 20th minute.
Ireland captain Shane Long had already demonstrated a clean pair of heels to the Georgia defence when he burst clear in the 15th minute but could not beat Loria with his flicked effort when one-on-one.
The visitors were complicit in their own downfall in the 20th minute when Ucha Lobjanidze's hopeless attempted backpass sent Long clear again and he lifted the ball beyond Loria before being cynically brought down on the edge of the box with a red card the only possible outcome.
Back-up keeper Omar Migineishvili was sent on from the bench and was immediately called into action to tip James McClean's goal-bound free-kick over the bar, before Long rifled a half-volley narrowly wide of the post moments later.
Trapattoni's men laboured through much of the remainder of the first period despite their numerical advantage, before finally breaking the deadlock as McClean's curling free-kick towards the far post was headed down into ground and beyond the flailing dive of Migineishvili by Richard Keogh.
Ireland's record goalscorer Keane was sent on at the interval to join Given in the record books, with a new landmark in his sights against Group C minnows the Faroes at the end of next week.
Trapattoni's men doubled their advantage in the 48th minute when Wes Hoolahan played in McClean behind the defence. The Sunderland midfielder's low cross was missed by the keeper and Simon Cox arrived at far post to drive home.
Long had a third chance to get his name on the scoresheet after another great pass from Hoolahan in the 58th minute, but again he was denied by Migineishvili as he elected to shoot rather than round the keeper.
Defender Richard Dunne, who confirmed earlier that he will leave Aston Villa this summer, came on for his first appearance of season after an injury blighted campaign to warm applause from the sparse home crowd.
Georgia's defence then blundered twice to allow Keane to take his tally for his country to 56 with two goals in the final 13 minutes as he first tapped home from Conor Sammon's low cross before curling beyond Migineishvili after another lapse presented the hosts with possession.