The game turned in the 20th minute when Georgia had goalkeeper Giorgi Loria sent off for bringing down Shane Long after he was sold short by a backpass, and from there on Ireland had it relatively easy as they prepare for next week's World Cup qualifier against the Faroe Islands.
Keane went on as a substitute at half-time to move level with Shay Given on 125 caps, and he soon added his 55th and 56th international goals, adding to strikes from Richard Keogh - his first for Ireland - and Simon Cox.
"Of course it's always nice to score goals as a striker," Keane told Sky Sports. "It's very important for the confidence.
"I felt a bit sorry for them with the red card, it was a shame and it killed the tempo of the game. We wanted a bit of a test before next week's game but it gives us confidence."
Asked about the caps milestone, he added: "If you asked me 10 years ago would I get this many caps, I'd say you were crazy. I'm obviously delighted and its something I can look back on in years to come but at the moment I just hope to get a few more."
With Keane starting among the substitutes, Shane Long captained the side for the first time as he is suspended for Friday's qualifier and instead heading off to get married.
"It's an unbelievable honour," he said. "At half-time I offered Robbie the band but he said, 'No, it's your night, you keep it'. I'm delighted, it's a big honour and it's nice to get a win.
"It would have been nice to get a goal as well but that's the way it goes."
Long was the man trying to latch on to a loose backpass when he was brought down by Loria to bring about the 20th minute red card.
"I hit it past him and the clash was inevitable," he said. "I don't think he meant any malice but the rules of the game are the rules of the game."
Long will now leave the Irish camp due to his suspension.
"It's a shame," he added. "I would really like to play alongside Robbie next week but I managed to pick up two yellow cards so I'm going to miss it and instead I'm going to get married in a couple of weeks."
Ireland face the Faroe Islands on Friday night and after an encouraging week of friendlies - a 1-1 draw against England at Wembley followed by today's easy win - Keane is eager to make it count.
"If gives you confidence and it's important to win games," he said. "Next week against the Faroes people expect us to win the game and really we should, but to be honest we can't take it too lightly.
"You have to give the teams a lot of respect and do it in the right way on the pitch. Hopefully we get the three points. It's been a very good week for the players but the main game is next week. These two games mean nothing apart from pride."