There's another option that falls somewhere in the middle or your two examples:

use warnings;
use diagnostics;
use strict;

my @array = ("8.foo", "6.bar", "7.baz",
"5.biz", "3.fizzle", "0.fro", "9.boz");

print join "\n",
sort {by_number($a) <=> by_number($b)} @array;

sub by_number {
        my $value = shift;
        if ($value =~ m/^(\d+)/) {
                return $1
        }
}
[download]

Now, of course this is going to be slower than the ST, but whether the optimization is necessary or not depends on a lot of things. Testing on my machine with an array of 70,000 elements, the ST takes 1.6 seconds and this one takes 5. That makes the ST 3.3x faster, but the increase might or might not be worth the more complex code. 5 seconds to sort 70,000 elements is not too shabby, and if the actual data is going to have far fewer, then the extra complexity just might not be worth it.