Parrott continued his superb run of recent form for club and country with a spectacular individual goal to get the hosts off to a perfect start back in Dublin.
The Real Betis hitman then slotted home from the penalty spot just before half-time as he moves onto 14 international goals.
However, as Ireland tired after the restart, Austria hit back with two late goals to earn a point at the Aviva Stadium in the third round of games in this Nations League series.
Parrott was brought off by Hallgrimsson in the closing, and the Icelander confirmed that was to protect him for the October 4th clash with Israel, which will be played behind closed doors in Serbia.
"It's a shame his goals did not give us a win, but I think you will be watching the first one for years to come.
"He had a few knocks, and was getting tired, and we need him in three days. Troy has a special gift going forward and scoring goals, but what I always see in him, that I don't see in many other attackers is his defensive discipline and hard work.
"I hope he continues to improve, but it's magical for Irish football to have him in a green shirt."