Jonathan Walters doubled the Republic’s lead in the 68th minute when he scored his first international goal before Robbie Keane netted the third three minutes later.

Estonia were then reduced to nine men after Raio Piiroja was dismissed before Keane scored his second from the penalty spot after Ats Purje fouled Stephen Hunt.

The result means the Republic take a commanding lead into the second leg at the Aviva stadium on Tuesday where Keane is confident his side can finish the job.

“We came here to get a result and full credit to the players they put in a great performance from the start.

“They had a couple of players sent off but I think we had the job done before that. We got the early goal and managed to kick on from there.

“To come here and win 4-0 is a great result.

“The confidence that we have in the squad and the way we played in the whole campaign we deserve to go through and we are looking forward to Tuesday night now.”

Keane was also full of praise for his fellow goalscorers.

“Jonathan Walters is brilliant. He’s a handful and he deserved to score tonight.

“Keith was superb from the start and he drove us on from midfield.”

However, the LA Galaxy striker refused to admit the job is done ahead of the second leg.

Andrews admitted the result had come as a bit of a shock.

“It hasn’t sunk in yet,” the goalscorer said. “It’s hard to believe we’ve come here and won 4-0.

“To get four goals and keep a clean sheet is a fantastic result.

“I thought we played very well tonight, harried them and fortunately got the result.

“If we keep a clean sheet it will be a fantastic night (at the Aviva). Over the past few years this group has really come together.”

Republic of Ireland manager Giovanni Trapattoni congratulated his team after they all but booked their place in the Euro 2012 finals.

“We are proud of our players because of their commitment, their mentality and their belief.

“They believe what we ask them.

“90 minutes is always difficult and now we can say we have a good result.”