After Given had pulled off a superb save to deny Cyprus striker Ioannis Okkas at the GSP Stadium in Nicosia on Saturday night, Keane did what he does best at the other end with seven minutes remaining to snatch a precious 2-1 victory.
The win sends the Republic into next month's showdown with reigning world champions Italy knowing top spot in the group and automatic qualification will still be up for grabs no matter what happens when Marcello Lippi's men meet third-placed Bulgaria in Turin on Wednesday evening.
Keane's late header was his 40th goal in 92 senior international appearances and Given, who has spent more than a decade in the Ireland squad with the Tottenham striker, is well aware of his abilities. He said: "They say the hardest part of football is scoring the goals, and Robbie has got a great knack of being in the right place at the right time and sticking the ball away.
"He deserves great credit. He's the captain and a leader as well, and he deserved his goal. That's his 40th goal for Ireland and he is streets ahead of any other goalscorer. It's fantastic for him. It was a massive, massive goal. He has scored so many down the years, important goals, and he nicked another one on Saturday night."
If Italy beat Bulgaria on Wednesday, they will go four points clear at the top of the group and will be even hotter favourites to see off Ireland's challenge. However, Given and his team-mates believe there is enough football yet to be played to give them a chance of springing what would have been considered a major shock when the draw was made.
He said: "We have got to believe we can do it. Why not? We will see how Italy and Bulgaria go on Wednesday night, and then it is going to be a massive game at Croke Park on that Saturday in October. You never know."
Given and Keane are veterans of the 2002 FIFA World Cup campaign which attracted as many headlines for the Irish for what happened off the pitch as for what happened on it. However, it remains a highlight of the 33-year-old Manchester City keeper's career and he is desperate to have another crack at the biggest tournament of all.
Given said: "We are not there yet, but it's the biggest chance we have had for a number of years now of qualification, so it is getting exciting. We knew how big a game Saturday night's was for the whole country, we knew what was at stake and we were delighted to walk away with three huge points, and roll on the Italian game.
"It was one of the highlights of my career to represent Ireland in the World Cup finals in 2002, and it still is. But I would like to go back again. South Africa would be fantastic, and not too far for the fans either. It would be a great occasion if we could do it."