Brozovic added the second goal in the 34th minute in similar fashion, sneaking into the area to finish off another centre from the left by Mario Mandzukic.
The open, attacking nature of the game continued in the second period with both sides hitting the woodwork and missing a string of scoring opportunities.
Experienced Israel midfielder Yossi Benayoun, recalled by caretaker coach Alon Hazan, returned to the international arena.
Benayoun went on as a substitute in the 77th minute to win a record 97th cap for Israel who have failed to qualify for the European Championship finals in France in June.
(Writing by Ori Lewis; Editing by Tony Jimenez)
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