Giovanni Trapattoni's side have all but booked their place at Euro 2012 with a resounding victory after their opponents had a man sent off in either half
Keith Andrews, Jon Walters and Robbie Keane, who bagged a brace, all scored to take advantage of Andrei Stepanov and Raio Piiroja's red cards and ensure that the boys in green would go into Tuesday's second leg in Dublin with a huge advantage.
The hosts seemed overawed by the occasion right from kick off and bustling Ireland forward Walters looked take advantage of the uncertainty.
Although Estonia began proceedings in a nervy manner, they almost opened the scoring when Konstantin Vassiljev’s long-range effort deflected off Andrews and looped over Shay Given and onto the roof of the net.
However, Ireland, rather crucially, got their noses in front before their opponents managed to fully settle. And it was energetic midfielder Andrews who met Aiden McGeady’s teasing centre with a thumping header which flew past goalkeeper Sergei Pareiko’s despairing dive.
McGeady was causing problems down the left wing, and one trademark run ended when he was cynically tripped by Stepanov, who, in a moment which would be given further significance later in the half, was booked.
At the other end, Tarmo Ruutli’s side were finding their feet, with star player Vassiljev beginning to get on the ball and drive at the Irish defence.
In the 22nd minute, he unleashed a thunderous strike from distance which whistled inches wide of Shay Given’s right-hand post.
The complexion of the game would have been entirely different had the 27-year-old’s effort nestled in the net, but as it was, the match would irretrievably turn in their visitors’ favour when Stepanov was sent off for a second bookable offence in the 34th minute.
The centre-back’s mistimed tackle saw him crash into Keane, resulting in a second booking, which could easily have been a straight red due to the foul denying a goal-scoring opportunity, and leaving his side’s Euro 2012 hopes hanging by a thread.
On my head son | Andrews nods in the opener from McGeady's cross
Despite the numerical disadvantage, Estonia started the second 45 in a determined mood and went close to restoring parity when Vassiljev’s low free kick was deflected narrowly wide of his own goal by Richard Dunne.
But they could not maintain the intensity of their search for an equaliser and eventually crumbled in the closing 30 minutes of the match.
In the 67th minute, Walters doubled his side’s advantage when he nodded home Keane’s clever lofted pass to the far post after McGeady’s strike had been weakly parried by Pareiko.
And the Estonia goalkeeper failed to cover himself in glory again four minutes later when he misjudged the trajectory of Andrews’ free kick and stuck out a leg to block, leaving Keane with the simple job of rolling the ball into an empty net.
The hosts’ misery was compounded in the final 15 minutes when they were reduced to nine men after captain Piiroja was shown a second yellow card before Keane wrapped up the win with a cool penalty in the 88th minute.
The sides meet again in the Aviva Stadium, Dublin on Tuesday, November 15 for what now seems a formality in the second leg of the play-off.