Speaking on Monday, Hallgrimsson admitted he would accept a sub-par performance if it meant beating Armenia after a battling defensive display failed to deliver a point against Portugal in Lisbon on Saturday.
And that's what he got.
Until Barseghyan saw red mist, the Republic of Ireland failed to lay a glove on the 103rd-ranked visitors in a flat, disjointed performance that evoked memories of Yerevan and attracted boos from the home crowd in Dublin at half-time.
And while Armenia did not carry the same level of threat as they did last month, the Republic of Ireland were fortunate to be level at the break after Spertsyan - who already has three career goals against the Boys in Green - failed to convert Kamo Hovhannisyan's cross at the back post.
But once again, Hallgrimsson's side were helped by ill-discipline from the opposition. Last month, they trialled Hungary at home but managed to rescue a draw after Roland Sallai was sent off for a reckless challenge on O'Shea.
Here, it took Barseghyan's dismissal for the Republic of Ireland to show some urgency, with Collins, O'Shea and Ferguson all denied before the latter finally found the breakthrough.
Avagyan also produced an excellent point-blank save to stop Adam Idah from further improving the Republic of Ireland's goal difference.
While the result will please Hallgrimsson, the Icelander will know his players cannot afford to produce a similarly passive and listless performance in next month's final two qualifiers against Portugal and Hungary.
But he will focus on the positives after the fifth win of his reign, which included Ferguson scoring in his fourth home international in a row, becoming the first Republic of Ireland player to manage that since Robbie Keane in 2014.
While Troy Parrott is pushing for a start after returning to fitness and Idah looked sharp after being introduced in the final 10 minutes, Ferguson is crucial to the Republic of Ireland's chances of upsetting Portugal next month.
Of course, it could have been an even better night for the Republic of Ireland had Portugal held on to beat Hungary.
After going behind early, two Cristiano Ronaldo goals turned the game in Portugal's favour before Szoboszlai's injury-time leveller.
It means that if Hungary beat Armenia in their next game, the Republic of Ireland must earn at least a point against Portugal to keep their play-off hopes alive before travelling to Budapest in their final game.
There are permutations aplenty and the odds remain against the Republic of Ireland, but they remain in the hunt - and that is all they could have asked for after a rocky start to the campaign.
Image source, Getty Images
