Actually, I seem to recall from his book that Lindbergh slept periodically (probably even more than he realized), but periodically woke up, and did so often enough to keep on course. When a person is really tired, they can doze off many times for substantial periods of time and never actually be aware of it. It might seem like you've been asleep for a total of only a few seconds, and in fact you might have been asleep for minutes or hours overall.
What I find interesting about this incident is that it's getting a lot of media coverage, whereas the nearly simultaneous problem with the Delta aircraft that landed on an active taxiway is being practically ignored. Given that landing on a taxiway presents a vastly larger risk of an accident with loss of life than just dozing off for a few minutes, I have to wonder exactly what motivates the media to cover one story but not another.