The Birmingham midfielder struck his first senior international goal after 76 minutes to edge the Irish past Vardan Minasyan's men at the sweltering Yerevan Republican Stadium.
No-one will have been more delighted than captain Robbie Keane, who passed up a glorious early chance, had a goal ruled out for offside and then hit the post on a night when things did not go for him in the final third.
However, there was as much relief as pleasure as he and his team-mates left the pitch having been put to the test by their hosts.
Armenia gave as good as they got and although goalkeeper Shay Given had few saves to make which genuinely taxed him, the home side were quick, direct and technically gifted and were certainly no push-over.
Indeed, in playmaker Henrikh Mkhitaryan, they had arguably the best player on the pitch, and the Republic will hope Armenia can take points from some of their rivals when they visit the Yerevan Republican Stadium.
The win sends Ireland into Tuesday's home clash with Group B minnows Andorra knowing a perfect start would set the up very nicely for what lies ahead.
Manager Giovanni Trapattoni admitted at his pre-match press conference in Yerevan that he would happily settle for a 1-0 win from what he promised would be a tricky fixture, and if anyone doubted his voracity, they were soon disabused of the notion.
Armenia, who have beaten both Poland and Belgium in their capital city in recent years, were far from over-awed by the task with which they were presented, and with the impressive Mkhitaryan, Shakhtar Donetsk's recent £5.8million acquisition, pulling the strings behind lone striker Yura Movsisyan, they made life intensely difficult for the visitors.
Mkhitaryan treated Derby midfielder Paul Green to a torrid welcome to competitive international football, while wide men Edgar Malakyan and Levon Pachajyan kept full-backs John O'Shea and Kevin Kilbane on their toes throughout the opening 45 minutes.
For all that, the Republic could have gone in at the break comfortably in front.
Keane might have put them ahead within eight minutes, but volleyed agonisingly wide from Kevin Doyle's flick-on with just goalkeeper Roman Berezovsky to beat, and he thought he had done so 10 minutes before the break when he shot home from Glenn Whelan's free-kick, only for an offside flag to ruin his celebrations.
However, perhaps the best chance fell to central defender Sean St Ledger, whose powerful 22nd-minute header from an Aiden McGeady corner was palmed away by Berezovsky.
Given had to save from Karlen Mkrtchyan and Pachajyan in quick succession, and he was grateful to see Movsisyan volley over 14 minutes before the break.
Trapattoni sent his side back into battle knowing they were in a game, and they were almost caught out within five minutes when Movsisyan combined well with full-back Artak Erdigaryan, but then overhit his through-ball to the supporting Mkhitaryan.
Mkhitaryan forced another save from Given and Mkrtchyan hooked just wide with Armenia sensing a genuine opportunity, and there was an anxious moment for the Ireland goalkeeper when defender Richard Dunne's headed clearance looped just over his own crossbar
But as the home side forged forward in search of the opening goal, they left space at the back and Doyle almost exploited that 19 minutes from time with a powerful drive which Berezovsky had to palm away.
In the meantime, Trapattoni had replaced McGeady with Fahey, and it was he who finally put the visitors in front with 14 minutes remaining.
Armenia could not clear their lines as Keane and then Doyle made nuisances of themselves, and when the ball broke to the Birmingham midfielder, he smashed it past Berezovsky to snatch victory.
In a tense finish to the game, the home side penned Ireland back inside their own half, but stout defence won the day as Trapattoni's men once again ensured that one goal was enough.