Well, you'll have to be more verbose...
$stmt = "DELETE FROM myTable WHERE this='$this_val' AND this_other_thing='$this_other_val'";
You can keep on going, adding more and more criteria to it till you finally narrow in on that one row.
Generally speaking, it's a good idea to have atleast one indexable column in there so you can better associate a row with other data in other tables, but hey... live and learn.