The two subroutines in the code below achieve the same thing in different way. As others have pointed out, the mode +< (or O_RDWR with Fcntl module) is the one you need instead of +>> (the latter is still possible, just harder) for the first sub. The second sub uses Tie::File module that makes file operation is as simple as array operation.

The code (file locking is omitted intentionally):

#!/usr/bin/perl

use strict;
use warnings;

my($rdwr_file, $tie_file) = @ARGV;

with_rdwr();
with_tiefile();

sub with_rdwr {
    open DAT, "+<$rdwr_file" or die "can't open $rdwr_file: $!\n";
    my $last = (<DAT>)[-1];
    if ($last =~ /(\d+)/) {
        my $new = $1 + 1;
        seek DAT, 0, 2 or die "Can't seek in $rdwr_file: $!\n";
        print DAT $new, "\n";
        print "new value for $rdwr_file: $new\n";
    }
    close DAT;
}

sub with_tiefile {
    use Tie::File;
    my @lines;
    tie @lines, 'Tie::File', $tie_file or die "can't tie $tie_file: $!
+\n";
    my $last = $lines[-1];
    if ($last =~ /(\d+)/) { # sure, testing on $lines[-1] saves a line
        my $new = $1 + 1;
        push @lines, $new;
        print "new value for $tie_file: $new\n";
    }
    untie @lines;

}
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The run:

$ echo 0 > rdwr
$ echo 0 > tie
$ cat rdwr
0
$ cat tie
0
$ perl prog.pl rdwr tie
new value for rdwr: 1
new value for tie: 1
$ cat rdwr
0
1
$ cat tie
0
1
... and some executions later..
$ cat rdwr
0
1
2
3
4
5
$ cat tie
0
1
2
3
4
5
[download]