I cannot replicate your problem with the posted code. The following code, taken almost entirely from your OP, works for me:

#!/usr/bin/perl
use strict;
use warnings;

while(my $evalue = <DATA>){
    chomp $evalue;
    if($evalue < 0.001){
        print $evalue, "\n";
    }
}
__DATA__
1e-005
2e-090
0.00
0.67
1.0
4e-065
[download]

The main changes are the file handles. Note that your chomp was not given a variable, and hence was operating on $_ instead of $evalue.