Italy, who held holders Spain to a one all draw in their opening game, started the encounter brightly in Pozanan.
After missing several chances they went ahead after 39 minutes.
Andrea Pirlo became the first player to score directly from a free kick at a European championship since 2004 when his 25-yard curling effort dipped over the wall and past Stipe Pletikosa, despite the keeper’s best efforts to claw it out.
Croatia refused to sit back and gradually forced their way back into the tie.
It wasn’t until the 72nd minute that Croatia and their fans got what they had been looking for.
Italian defender Giorgio Chiellini completely misjudged an inswinging cross from Ivan Strinic allowing Mario Mandzukic to pounce.
The striker clinically controlled the ball at the near post before firing his shot past Gianluigi Buffon, who from close range had no chance.