We used to believe dreaming always happened in REM sleep, but we've later discovered that's not actually true. It can happen in the other stages as well, most often in NR3 and least often in NR1.

But it's also possible it was "hypnogogic hallucinations," which can be a dream-like state as you're falling asleep. If you've had the experience of thinking about something and suddenly jerking awake (hypnogogic jerks) and feeling like you were in a light dream, it was probably that an not a "true" dream (if the two can even be fully distinguished, I'm not up to date on the research). For me, whether by jerking awake, or rolling over, or something else, I often "wake up" from a hypnogogic hallucination and find myself feeling well-rested, regardless of how tired I was just a few minutes previous.