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Giovanni Trapattoni's side were never in danger of an embarrassing defeat against the part-timers from Andorra after racing into a two-goal lead in the first 20 minutes thanks to strikes from Kevin Doyle and Aiden McGeady.
That opening salvo meant the result was never in doubt in the tiny principality's Estadi Comunal.
But there was bad news from Slovakia, where Russia's 1-0 win realistically ended Ireland's hopes of finishing first in the group.
The Russians are two points clear at the top and can seal automatic qualification with a draw at home to the woeful Andorrans on Tuesday.
In that case second placed Ireland would have to settle for a play-off spot, providing they can avoid defeat in their final fixture against third placed Armenia in Dublin on Tuesday.
A win for Armenia would eliminate Ireland but the hosts will be favourites to get the point they need after their 1-0 victory in the last meeting between the sides.
In La Vella, Sean St Ledger had returned from suspension in place of the banned Richard Dunne, but Ireland's defenders rarely had to break sweat in the shadow of the Pyrenees.
The Andorrans had lost all eight of their Euro 2012 qualifiers, scoring one goal -- Cristian Martinez's strike against Ireland in Dublin -- and conceding 17.
With such a dismal track record it was no surprise to see Ireland take the initiative from the start.
Doyle's goal-bound shot was blocked by Ildefons Lima after 90 seconds and Robbie Keane nearly opened the scoring when he burst into the penalty area and lofted a shot onto the top of the crossbar after his initial effort had been saved.
But Trapattoni didn't have to wait long for the first goal as Ireland's pressure told in the seventh minute when John O'Shea headed a corner down for Wolves striker Doyle to hook in from close-range.
Play was briefly held up to fix a hole in the Andorran net but there was no plugging the gaps in the home defence.
Ireland were overwhelming Andorra with wave after wave of attacks and it was no surprise when the visitors notched a second goal in the 20th minute.
This time it was a lack of concentration that let Andorra down as Glenn Whelan opted to pass to McGeady rather than shoot from a free-kick. The move caught Andorra's defence day-dreaming and McGeady had time and space to fire home via a deflection off Lima.
There was a blow for Ireland when left-back Stephen Ward was booked for diving, ruling him out of the final qualifier against Armenia.
With the game all but over, Ireland were content to conserve as much energy as possible ahead of the crucial clash with Armenia.
That made for a drab second half but even then Ireland nearly extended their lead when Josep Antonio Gomez blocked bravely from Keane and then dived low to his right to tip McGeady's stinging shot on to a post.
Keane passed up a glorious opportunity to claim his 52nd goal for Ireland with 61 minutes gone when he blazed over from Damien Duff's pass.
O'Shea went close to adding his name to the scoresheet when he headed just over from Duff's corner in the 74th minute.