An own goal by Valeri Aleksanyan after 43 minutes and a second from Richard Dunne on the hour put Ireland in control before Henrik Mkhitaryan pulled one back almost immediately for Armenia.
The visitors were harshly reduced to 10 men when goalkeeper Roman Berezovsky was wrongly sent off by Spanish referee Eduardo Gonzalez after 26 minutes for handball outside his box when TV replays showed he chested the ball clear.
That severely dented their hopes of winning and staying on course for a first ever finals appearance, and the error was compounded by the referee who had allowed play to continue when it appeared Irish striker Simon Cox did handle the ball moments before the goalkeeper was wrongly adjudged to have done so.
If that balanced out Henry's handball which cost Ireland the chance of reaching last year's World Cup when Henry's infringement in the build-up to France's winning goal went unpunished, Cox was not saying.
"It was an unbelievable night for Irish football," he said.
"We needed to at least get six points out of six [from the final two games] and we got them and we've got what we wanted in the end - a play-off place."
Asked if he handballed in the incident that led to the red card, he added: "No, it came over my shoulder and I brought it down as well as I could, and if it brushed my shoulder, well some you get and some you don't."
However Berezovsky's debutant replacement Arsen Petroysan was first beaten by Aleksanyan's own goal before half-time and then by Dunne in the second half to give Ireland the points they needed to finish behind Russia. Armenia, who played well in the second half of the campaign, finished third.
Ireland coach Giovanni Trapattoni said he did not think his side were lucky but was full of praise for Armenia whose run of form saw them rise from outside the top 100 in the world rankings before qualifying began to 44th now.
"Armenia played very, very well with 10 men. Before we said Armenia is one of the best in the group, their defenders play football like midfielders... for us it is a great result," the Italian told reporters.
Armenian coach Vardan Minasyan did not take any questions from journalists, saying simply that he was proud of his players. His side started and finished the brighter but Ireland ultimately used their 50-minute extra man advantage well.
The hosts carved out few chances until winger Damien Duff's smart cross found Kevin Doyle at the front post and after the Wolverhampton Wanderers striker failed to flick it in, Aleksanyan bundled the ball into his own net.
Ireland began finding more space in the second half with first Cox and then Keith Andrews going close before Doyle failed to connect with another near post cross and replacement keeper Petrosyan's flap allowed Dunne to make it 2-0.
Shakhtar Donetsk forward Henrik Mkhitaryan pulled a goal back for the visitors two minutes later, linking up neatly with striker Yura Movsisyan to end Ireland's run of eight successive clean sheets.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.