Prior to the match, Italy coach Cesare Prandelli said the return of Mario Balotelli for the first time since UEFA EURO 2012 was the key to getting his team firing, only to lose the Manchester City man once again to a fever.
And in his absence, Italy looked short of cutting edge as they struggled to break down their hosts and found themselves on the backfoot for much of the match.
The early signs had been promising for Italy, with Pirlo's fourth-minute free-kick forcing Roman Berezovsky into an excellent save after Hrayr Mkoyan was penalised for handball.
It was from another set-piece that they took the lead in the tenth minute, with Mkoyan yet again the villain for Armenia as he handled in the area, earning a yellow card and conceding a penalty which Pirlo placed in the bottom left-hand corner.
But while they had benefited from Mkoyan's overeager hands, Italy were failing to create anything themselves, and it was Armenia who looked the more dangerous in front of goal against a rather flat performance from the visitors.
Aras Ozbiliz's curling free-kick forced Gianluigi Buffon into action in the 14th minute before Artur Edigaryan and Artak Yedigaryan missed the target with efforts from the edge of the area.
That at least stirred Italy into action, but Berezovsky comfortably held Sebastian Giovinco's shot in their best opening.
Armenia continued to attack, with Ozbiliz and Robert Arzumanyan both working Buffon before the break, while Riccardo Montolivo lashed wide just before the break.
Giovinco blasted over from close range early in the second half, but it was hardly a sign of a vastly improved Italian performance and instead Armenia continued to enjoy the better of the chances.
Mkhitaryan fired wide from a good position before Davit Manoyan's effort forced another good save from Buffon, who stretched to push it around the post.
The Juventus veteran was less convincing in handling Ozbiliz's 58th-minute shot but did enough to keep it out.
Domenico Criscito's shot on the hour mark went wide for Italy, but some good news was coming for Prandelli as De Rossi made up for his earlier miss by powering in a header from Pirlo's cross in the 64th minute.
A Pirlo corner moments later almost brought a third but Montolivo fired over.
Instead, it was Italy who prospered, and after Emanuele Giaccherini had fired over Osvaldo headed in a third with 10 minutes to go, getting up to meet De Rossi's cross.