Is the kit lens that comes with the Nikon D5100, sufficient for portraits?

Obviously any lens will take a portrait… But what lens exactly, is good for quality portraits, with a very pleasing, Shallow D. O.F? Would the kit lens suffice?

If you shoot wide open, yes. People who are serious about portraiture often invest in a 50mm f1.8 (the standard lens for 35mm) for this purpose, but the kit lens (18-55mm) will get you started.
It's amazing what you can achieve with a subject in front of a plain background.

Shallow DOF and portraits.no, the kit lens is not good at that. The nikon 50mm f1.8 AF-S is the better choice.

You are correct that any lens will do portraits if you know how to operate it and light your subject.
A 50mm f/1.8 is a good lens but it's limits are it's too tight for most everything else you might want to
do.

I'd do some serious reading and lots of practice about operating lenses, aperture, focus, distance from subject, all that kind of stuff. Also read about light, probably the most important part of any good
photo outside of photographer skills.