Georgia keeper Giorgi Loria was sent off on 20 minutes after upending striker Shane Long - prompting Romanian referee Sebastian Constantin Coltescu to produce a red card.
Derby defender Richard Keogh opened the scoring three minutes before the break with his first senior international goal.
Nottingham Forest striker Simon Cox extended the side's lead three minutes after the restart after good work by James McClean.
Substitute Robbie Keane scored twice late in the game, claiming his 55th international goal from point-blank range with 13 minutes remaining before taking his tally to 56 three minutes from time.
Keane's double sealed a comfortable victory during the low-key friendly.
The 32-year-old is expected to lead Ireland into a World Cup qualifier battle with the Faroe Islands next Friday evening.
He said the win will be a confidence booster ahead of the qualifier.
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.
"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."
"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."
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 it's something I can look back on in years to come but at the moment I just hope to get a few more."
"It's an unbelievable honour," Captain Shane Long said after the game.
"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 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."
Manager Giovanni Trapattoni had made nine changes to the side which drew against England at Wembley on Wednesday night.