Croatia, which finished third in the 1998 World Cup, took the lead in the 14th minute through an own-goal by Spain defender Pablo Ibanez, but Spain rallied Mariano Pernia in the 62nd and Fernando Torres two minutes into second-half injury time.
Croatia coach Zlatko Kranjcar made six substitutions throughout the match.
The Brazilian coach has been saying he is expecting a tough World Cup opener against the Croats, who "have prepared well ahead of the competition."
Parreira said Brazil has observers in all matches played by the team's group-stage opponents, which include Australia and Japan, according to the AP.
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