Starting the night knowing that they would have to better Norway's result against Italy, Ante Cacic's side did their part and were helped out by the Azzurri, who came from behind to claim a 2-1 win in Oslo.
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The difference between the two sides was clear from the first whistle, but Croatia were frustrated in front of goal early in the game as Andrew Hogg made a fine save to keep out a low effort from Nikola Kalinic.
It was the Inter winger who broke the deadlock as he reacted to a clearance with a powerful effort from the edge of the box which took a deflection on the way to beating the helpless Hogg.
Despite their dominance, Croatia were almost shocked by an equaliser before the interval when Alfred Effiong found the space to head over from a corner.
Hogg continued to be a busy man in the second half as he made saves to deny both Marko Pjaca and Perisic as Malta looked to keep alive their hopes of adding to a tally of just two points from the campaign.
It was a strong finish from Malta as Andrei Agius met a free kick to test Danijel Subasic, who pushed his effort to safety as Croatia claimed the victory on the way to booking their spot at the tournament.