Richard Dunne was the Republic's hero once again as his goal secured the hosts second place in the group.
The Aston Villa defender, whose man-of-the-match defensive display in Russia last month helped to secure a point, ensured all three went Ireland's way in their final Group B game with a 60th-minute goal which cemented them in second place on a night when both sides had a man sent off.
Much of what could have gone the Republic's way before the break did so with the dangerous Armenians having keeper Roman Berezovsky sent off with just 26 minutes gone.
The visitors' plight deepened a minute before the break when defender Valeri Aleksanyan turned Damien Duff's cross into his own net, and when Dunne bundled home a second on the hour, the game looked to be over.
But Henrikh Mkhitaryan's strike two minutes later ended Ireland's run of eight clean sheets and sparked concerted fightback, and the final whistle was greeted with as much relief as joy.
Giovanni Trapattoni, whose own future as manager seems inextricably linked to the success or otherwise of this campaign, saw his decision to play Simon Cox rather than Shane Long pay off, although he will have been less pleased with Kevin Doyle's rather harsh dismissal for a second bookable offence.
Doyle would have missed the first leg of the play-offs as a result of his first booking anyway, but his manager will hope skipper Robbie Keane is fit enough to play or the Italian will be without both his first-choice frontmen.
Almost two years ago, the Republic's World Cup dreams were ended by a handball decision - or rather a non-decision - as France scraped past them with the help of a large slice of good fortune.
That hurt has festered ever since, and the prospect of another crack at the lottery of the play-offs is one which brings as much trepidation as excitement and hope.
However, beggars cannot be choosers and having pushed Russia all the way, Trapattoni's men knew heading into tonight's game that a draw would be enough to book their place in the play-off.
Armenia arrived in Dublin brimming with confidence after three successive qualifying victories and 11 goals, and there was more than a hint of concern around the Aviva Stadium, if not inside the home dressing room, before kick-off.
But having finalised his preparations, the one thing Trapattoni could not account for was luck. And it was to his delight that when fortune chose to intervene, it did so in favour of the men in green.
In a tight opening half-hour, the visitors played as billed, passing the ball confidently with Marcos Pizzelli orchestrating from the middle of the field and Mkhitaryan and Yura Movsisyan ahead of him looking menacing.
However, it was Doyle who was first to work a goalkeeper, although he did not overtax Berezovsky with his 12th-minute effort after combining with Cox.
But the game turned with 26 minutes gone when Berezovsky's evening came to a premature conclusion.
Cox reacted first to a ball over the top before attempting to poke a shot past the advancing keeper, whose save was undoubtedly made outside the penalty area.
Spanish referee Eduardo Iturralde Gonzalez consulted his assistant before producing a red card as Berezovsky claimed in vain that he had stopped the ball with his chest.
Remarkably, replacement Arsen Petrosyan was also penalised for a similar offence a minute before the break, although having not prevented a goalscoring opportunity, he was only cautioned.
However, the substitute, who had come on for midfielder Edgar Malakyan in the wake of the sending-off, had already had to pick the ball out of his net when Aleksanyan did at the far post what Doyle had failed to do at the near and turned Duff's low cross home.
Armenia were determined to stick to their principles and continued to play enterprising football after the break.
But with Ireland starting to make their numerical advantage tell, the long-ball approach of the opening 45 minutes made way for a more expansive brand of football.
Doyle was twice denied by good blocks by defensive midfielder Karlen Mkrtchyan and Keith Andrews smashed a 25-yard piledriver a foot wide of the post.
Dunne looked to have secured victory when he bundled the ball home from close range after Petrosyan had palmed Aiden McGeady's teasing cross against him.
However, Mkhitaryan's snapshot two minutes later reduced the deficit and, with a little more composure, Movsisyan might have made the most of substitute Edgar Manucharyan's fine 66th-minute run across goal.
McGeady should have done better when set up by Duff seconds later, but Shay Given was relieved to see Manucharyan head inches over from Mkhitaryan's 70th-minute corner with the game far from over.
Doyle's 81st-minute dismissal for elbowing Mkrtchyan brought a disappointing end to an eventful evening, but the smiles on the final whistle were all Irish.