The Austrians had been beaten by Poland (home) and Israel (away) before gaining a 1-0 win over Slovenia on Friday evening.
Arnautovic was skipper for the night and grabbed the second and third goals in a 4-1 victory.
The No 7 was applauded from the pitch by both sets of supporters when replaced with a couple of minutes of the game remaining.
The victory ushed the Austrians into third in Group E, a point behind Israel, who were beaten 4-0 by Lukasz Fabianski’s Poland in Warsaw.
Josh Cullen was an unused substitute as Republic of Ireland edged to a 2-0 win over Gibraltar in Group D. That result in Dublin means Mick McCarthy’s side are five points clear at the top, having won three of their opening four matches.
Finally, Arthur Masuaku was in action on Sunday, starting for DR Congo in their goalless friendly draw with Burkina Faso – his country’s penultimate warm-up fixture for this summer’s Africa Cup of Nations finals in Egypt.
DR Congo meet Kenya on 15 June in their final friendly before tackling Uganda, the host nation Egypt and Zimbabwe in the group stage of the Cup of Nations.