Julio Cesar was beaten from the penalty spot in the third minute and let in a second 14 minutes later in the third-place playoff match.
It was his 12th World Cup game over two tournaments in 2010 and 2014.
The previous record-holder was Taffarel, who conceded 15 goals in 18 games across three World Cups. Taffarel played in 1990, 1994 and 1998, taking home a winner's medal in 1994.
(Reporting by Andrew Downie; editing by Ed Osmond)
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