Given your datasets, perhaps the following will be helpful (it correctly returns the one BLAST entry which contains a matching fasta header):

use strict;
use warnings;

my %headers;

while (<>) {
    $headers{$1} = 1 if /^>(.+)/;
    last if eof;
}

local $/ = 'Query= ';

while (<>) {
    chomp;
    print $/. $_ if /(.+)/ and defined $headers{$1};
}
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Usage: perl script.pl headerFile blastFile [>outFile]

The last, optional parameter directs output to a file.

The local $/ = 'Query= '; sets file reading to one BLAST entry ('record') at a time. The header info after Query= is captured and the complete entry is printed if that header is in the hash.