Midfielder Andrea Pirlo capped a majestic first-half performance by curling home a free-kick in the 39th minute as Italy took the game by the scruff of the neck and created a hatful of opportunities.
But their failure to take other chances, with Mario Balotelli the chief culprit, cost them dear when Mario Mandzukic punished slack marking by firing an equaliser in the second half of a game marred by Croatia fans throwing flares onto the pitch.
Slaven Bilic's team have four points from two games while Italy have two points. Spain, who have one point, face pointless Ireland in Gdansk later on Thursday.
Italy, whose open approach has provided a refreshing break from their traditional style of dour defence, had also let a one-goal lead slip against Spain, when they also started well but drew 1-1.
Coach Cesare Prandelli, whose team next face an Ireland side coached by his wily compatriot Giovanni Trapattoni, said they should have shown more of a killer instinct.
"When a side plays football, creates a lot of chances, they need to kill off the game but football is unique in the sense that one cross can ruin everything you've built up over the game," he said.
"We're still in this but we have wasted an opportunity here.
"There is a drop in our standard after the 60th minute," he added. "We need to see how we can manage our energy levels... I don't know why this is, when you're analysing the game you are not looking for justifications."
Italy stuck with their potentially brilliant but explosive pairing of Balotelli and Antonio Cassano in attack and, with Pirlo spraying passes around at will, they easily opened up the Croatia defence.
However, Balotelli, in particular, was guilty of wasting chances. Having forced Stipe Pletikosa into an early save with a snap shot, he wasted a tremendous chance when, after been picked out unmarked by Cassano, he dallied over his shot, giving the Croatia keeper a chance to make the save.
He then blew another chance when, with four players unmarked in the area, he tried to beat two defenders, slipped and lost the ball.
Lively midfielder Claudio Marchisio fizzed a 25-metre shot just over the bar and then forced a brilliant double-save by Pletikosa who dived at his feet to block the first effort and did the same from the rebound.
Italy were rewarded when the evergreen Pirlo curled a free-kick into the left hand corner from 25 metres six minutes before half-time. It was the first European Championship goal scored direct from a free-kick since 2004.
Cassano nearly grabbed a second goal for Italy before the break when he headed over from a corner but the second half was a different affair.
Croatia midfielder Luka Modric sounded the first warning shot when he fired over following the interval and, after Balotelli had scraped the bar with a ferocious 25-metre drive, Mandzukic levelled in the 72nd minute.
Ivan Strinic's long cross from the left picked out an unmarked Mandzukic, who had time to bring the ball down and score off the inside of the near post.
"We dropped too deep and we had to suffer a bit," said Pirlo.
Italy ended up having to cling on for a point as the fitter Croatians, backed by a large contingent of noisy fans, finished more strongly.
"We weren't good enough in the first half but we regrouped at halftime and in the second half we dominated and got a deserved equaliser," said Croatia defender Vedran Corluka whose side face Spain in their last game.
"We still have work to do in our last group match against Spain but we are confident of progressing to the quarter-f
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