The 28-year-old took just four minutes to get his country's opener in Luxembourg City – his third in the March international break after scoring twice against Slovenia last Friday.
Arnautovic bagged his 10th goal in his last 16 appearances for club and country by latching onto Sebastian Prodl's long ball and poking the ball beautifully over rooted goalkeeper Anthony Moris.
Austria won 4-0 as Florian Grillitsch (39'), Michael Gregoritsch (59') and Louis Schaub (84') all got on the scoresheet.
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