An edgy encounter in Gdansk was settled by a Jesus Navas goal as Croatia could notfind a way through the world and European champions.
Slaven Bilic's team played on the counter attack against the possessive Spanish but were hit with a sucker punch when a delightful Fabregas chip set Iniesta through to square for a Navas tap-in.
With a draw possibly enough to see both teams progress to the quarter finals, depending on the result between Italy and the Republic of Ireland, the first half was a tense affair with neither team opening up.
Mario Mandzukic appealed for penalty when he appeared to be caught on the edge of the box, but the referee waved away the 27th minute appeal.
With Italy winning in Poznan, Croatia became more adventurous and attacked Spain down the flanks. Luka Modric created the best chance when he crossed for Ivan Rakitic, but the 24-year-old Sevilla midfielder saw his firm header punched out by Iker Casillas.
The match was settled with just two minutes to play. Cesc Fabregas, a second half substitute, lifted a pass over the static Croatia backline for Iniesta to control and roll into the path of Navas, who had the simplest of tasks to score.
The result sends Spain through as group leaders but consigns Croatia to being knocked out before the quarter finals.
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