You don't have to clear customs but do have to go through internal security (not the same security as passengers arriving by ground to NRT).

There's a long thread on the Delta forum on NRT layovers, some are scheduled as short as 45 minutes.

I wouldn't be comfortable with anything less than an hour. I've been held up at very long security lines making connection to/from SIN flights. Note there are multiple security checkpoints at NRT terminal 1 and someone may know how to get to the other one (I seem to recall it was up/down some stairs).

Of course if you are flying CO 777s in economy, even a long, slow security line is like heaven compared to those torture seats.