Croatia went to the top of Group Eight but failed to score the many goals hoped for by their fans.
The next home game - against the Irish Republic on September 4th - is now even more important. The Croats need a win to stay in contention for a play-off place as they have now played two games more than rivals Yugoslavia.
To add to their problems captain Zvonomir Boban limped out of the action early with a thigh muscle strain that means he is likely to miss the game against Ireland.
Croatia had thrown away an early lead in a disappointing performance that saw Mario Stanic give the home side the lead in the 34th minute when he looped a header into the net after a cross from the right wing. Malta chased and tackled well throughout the game and in the 61st minute a fluffed clearance saw the ball break to David Carabott in the penalty area and he drove it into the net to take the game to a nervous conclusion. .
The Maltese goalkeeper Ernest Barry saved second half shots from close range by Davor Suker and substitute Alen Boksic and the Croatian pressure told when Zvonimir Soldo headed in from a 55th minute corner.
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