The Irish have suffered a series of play-off defeats since making their major tournament bow in 1988 with their only European Championships appearance, most painfully when Thierry Henry's infamous handball ended their World Cup dreams two years ago.
Friday's thumping victory in Tallinn made sure that run came to an end and neither Estonia stand-in captain Konstantin Vassiljev's second-half equaliser on Tuesday nor a generally flat Irish performance could spoil the celebrations in Dublin.
"I am very proud for many reasons... I am very happy for the players, for you and for all the people, all the supporters," coach Giovanni Trapattoni told a news conference.
"We can go into the tournament with confidence... I think never say never. In football there is no favourite."
Ireland, who have turned into a dogged and defensively sound outfit under the Italian, edged out Slovakia and Armenia in a tough qualification group to set up the make or break tie with the Estonians.
Although their plane tickets to Poland and Ukraine next June seemed all but assured prior to kick-off, Stephen Ward made Ireland's passage even more secure when he opened the scoring after 31 minutes.
DREAM BIG
Ward, almost ever present at left-back since scoring on his debut against Northern Ireland in May, struck from close range after a header by Wolverhampton Wanderers team-mate Kevin Doyle was parried into his path.
Estonia looked like a team who knew their chances of reaching a first major finals were over before they had set foot in Dublin but interrupted the party just before the hour when Vassiljev equalised.
Vassiljev, who had shown glimpses of the form that made Estonia shock play-off combatants before their capitulation last week, had Shay Given to thank after the usually reliable goalkeeper let a long-range effort squeeze under his body.
Estonia, missing first choice centre-backs Andrei Stepanov and skipper Raio Piiroja after they were sent off in the first leg, came closest to sneaking a winner when Given stopped a stinging Tarmo Kink strike.
However, a packed Aviva Stadium - full for a football international for the first time since opening last year - could not have cared less when the final whistle sounded and fans celebrated qualification 10 years to the day after beating Iran to reach the 2002 World Cup.
Trapattoni, who said it was best he did not join the team for a deserved beer after the game, told the supporters they should not be afraid to dream big when they arrive in Kiev or Warsaw next year.
"With this new group [of players], why not?", he replied when asked if Ireland could achieve what fellow underdogs Greece did in 2004 by winning the European Championships.
