Here's a way to do it using Tie::File, which also gives you the option of grabbing the previous n lines, not just the line immediately previous (maybe more useful if you need context in a log file.)

#! /usr/bin/perl

use strict ;
use warnings ;
$|++ ;

use Tie::File ;

tie my @file, 'Tie::File', 'test_h.dat' or die "Can't tie file: $!" ;

my $backtrack_lines = 1 ;
my $match = '' ;
for my $i ( 0 .. $#file )
{
    if ( $file[$i] =~ /baz/ )
    {
        $match = join "\n", @file[ ( $i - $backtrack_lines ) .. $i ] ;
    }
}

print $match ;

__END__
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_______________
DamnDirtyApe

Those who know that they are profound strive for clarity. Those who
would like to seem profound to the crowd strive for obscurity.
            --Friedrich Nietzsche