As no-contests go, this was about as enjoyable as they come. The Republic of Ireland's supporters turned out in their droves to toast an exciting new dawn. The hard work had been done in the play-off first leg – the 4-0 win in Estonia representing something beyond wild dreams – and Giovanni Trapattoni's players merely had to turn up to confirm their nation's place at Euro 2012.

They did more than that, against an Estonia team that once again looked limited. Ireland's professionalism did not desert them, as Dublin's night-spots braced themselves for rich pickings, and they signed off from a memorable qualifying campaign by extending their unbeaten sequence to 11 matches.

It might have irritated Trapattoni that Estonia were allowed to equalise out of the blue and even finish with more punch than they had shown over the rest of the tie. But it did not really matter. The die had been cast and, despite the game petering out, the crowd responded to what they had seen, particularly in the first half and, more generally, in every tie since the crucial 1-0 win in September of last year in the stifling heat of Armenia, which Trapattoni considered the most decisive moment.

A thumping home win here never seemed likely but this was no anticlimax and the players' post-match lap of honour felt like a love-in. Optimism followed each stride and the rapture from the stands made the senses bristle. Ireland had confirmed their qualification to a major finals for the first time on home soil.

"We'll shake a few people up next summer, that's for sure," the goalkeeper Shay Given told the crowd. They bellowed their approval. The Football Association of Ireland chief executive, John Delaney, looked tired and emotional. "It's made my day, my night, my life," he said.

This could have been considered as one of the biggest games of the Ireland players' lives and so the lack of tension, after the romp in Tallinn last Friday, felt weird. The dreams of everyone connected to the shirt had long since turned towards next summer. "Green with pride" read the signs around the ground at kick-off. The challenge for Trapattoni's players had been to maintain focus.

There was levity in the crowd. The paper aeroplanes, made from the signs on the seats, glided down, some with no little majesty, and it became a competition to land them on the pitch. There were plenty of successes, which drew hearty cheers. The sideshow was diverting and the first half drifted by on the breeze.

Ireland controlled it even if their trademark intensity was inevitably diluted. Damien Duff was sharp and Robbie Keane looked in the mood to plunder. Twice in the opening minutes Keane might have scored. He wriggled through after an error by Taavi Rahn but he could not round Pavel Londak and then, after the goalkeeper had only parried Duff's shot, he pulled wastefully wide of the near post.

Londak's shortcomings were highlighted when Ireland went ahead on the night, and so were those of the defenders in front of him. Kevin Doyle was allowed to find space inside the area to head Duff's corner goalwards and Londak's parry was more of a pat, which failed miserably to get the ball out of the danger zone. The left-back Stephen Ward gleefully gobbled up the chance. Trapattoni smiled and applauded. For once, he could enjoy the show.

There was a gentleness about the second half until Estonia provided an unexpected jolt when the captain, Konstantin Vassiljev, struck from distance; Given got down sluggishly and allowed the ball to slip through his fingers. It was only the second goal that Ireland had conceded in 11 matches; Given had been similarly at fault for the other one, scored by Armenia's Henrik Mkhitaryan from distance in Dublin.

Ireland raised the tempo. With Aiden McGeady on as a substitute, they threatened through Keane and Doyle and Richard Dunne thudded a header into Londak. By then, though, the action felt like it was getting in the way of the party. The celebratory mood was reflected in the ovations for Keane and Duff when they were substituted.

And then the final whistle sounded. Ireland had made the European Championship for only the second time. "The players deserve to have a party and to drink beer," Trapattoni said, "but maybe it's better that I don't see it. Greece won Euro 2004. With this group of players, why not? We have good options. It's not a dream."