The Spartak Moscow winger emerged as a genuine talent under O'Neill during his time in charge at Celtic and turned in one of his more impressive performances for his country in the 61-year-old's first game in charge of the national team, a 3-0 victory over Latvia on Friday evening.
Indeed, McGeady marked his 62nd senior appearance for Ireland with just his third goal, a skidding low drive from distance, and skipper Keane insists the midfielder has the ability to become a key player.
The LA Galaxy frontman said: "Aiden is a game-changer. He can create anything out of nothing - you see his goal.
"He knows himself he probably should score more goals. He is probably killing himself too much about that rather than just relaxing and enjoying himself and just playing with a bit more freedom.
"I think you will probably see that now he has a manager that he has worked under before.
"It was a great goal and hopefully he can continue that now and score a lot more goals, because he is a player who can do that."
Keane too found the back of the net - in his case for the 62nd time in an Ireland shirt - to give the Republic a 22nd-minute lead, and McGeady struck with 68 minutes gone before substitute Shane Long completed the perfect night for O'Neill as he launched his spell in charge.
The Latvians provided little resistance and life will be significantly tougher for the Republic in Poland on Tuesday evening, but Keane was delighted with the way they were able to build upon the positive atmosphere created by the appointment of the new manager and his assistant, Roy Keane.
He said: "It's been a great buzz for the last couple of weeks. Everybody is fairly excited about the changes that have happened, and when you have got two big characters like Roy and Martin involved in the set-up - in any set-up - it's going to create a massive buzz.
"We are lucky that they are here and we look forward to working with them. This was a stepping-stone in the right direction.
"Winning is a habit, so it's important. If we had lost the game, everybody is down in the dumps again, so it's important to give the whole country a lift and we did that.
"There's no competitive game for 10 months, but I'm sure the manager in that 10 months will be looking at a lot of players and seeing what he feels is best for him and for the team.
"I'm sure he will be doing a lot of homework."
Keane will now head off on a well-earned break with the MLS season over.
The 33-year-old scored 16 goals in 23 regular season appearances for his club, but was unable to help them retain their title as the bowed out of the play-offs at the hands of Real Salt Lake earlier this month.
Asked if the season had been one of his best, the striker, who has verbally agreed a new contract with the Galaxy, replied: "I won the championship last year; we got knocked out in the play-offs this year, so probably not.
"Personally for me, it's been a very, very good season, but it's not about individuals.
"It's always nice to score goals, but at the end of the day you want to win things. Unfortunately, we didn't get to the final this year, but it's been a decent season for me."