Goals from Marko Arnautovic, Michael Gregoritsch and Marcel Sabitzer helped Austria move to the top of the League A Group One after Denmark claimed an away 2-1 victory against France in the other game.
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Austria took the lead against the run of play just before half-time when Arnautovic made a solo run past the defence and took a shot from the edge of the box into the bottom right corner.
Substitute Gregoritsch doubled Austria's lead in the 54th minute on the counter attack with a fine first-touch strike, while Sabitzer made it 3-0 three minutes later.
Midfielder Ivan Perisic, young star defender Josko Gvardiol and defender Sime Vrsaljko were unavailable for coach Zlatko Dalic due to injuries as Croatia suffered their first defeat since the Euro 2020 finals last June.