A late Perisic goal and Milan Badelj opener denied Iceland their attempt to reach the World Cup knockout stage for the first time in top Group D.
Iceland needed a win to stand any chance of reaching the last 16, and their colourful support looked dejected as their side missed key chances late in the first half.
Alfred Finnbogason and Birkir Bjarnason both went close before the interval in Rostov-on-Don but Milan Badelj stylishly slammed home for Croatia after the break.
That forced Iceland to chase the game and, after Sverrir Ingason hit the bar, Gylfi Sigurdsson converted a penalty to level following Dejan Lovren‘s handball.
In the dying minutes, with Argentina leading Nigeria 2-1, Iceland knew a win would see them jump ahead of the South American side in second place.
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