Catching the last N'EX from Narita

I'm wondering if I have enough time to catch the last scheduled N'EX train at 21:44

My flight is scheduled to arrive from Korea at 20:55. Provided there is no flight delays or problems with baggage claims, would it be enough time to get from Terminal 1 and clearing customs to buy and catch the train?

Keep backup plan in mind. Keisei trains and Airport bus.

If there are no problems and your luggage is quick or first to show and customs doesn't check you, then yes, there is time. But this is an important question: have you been to Narita before? Do you know exactly where everything is? If you're very familiar with the terminal and can make a beeline to exactly where you need to go, then you'll have no issues, provided everything else beforehand runs smoothly. If you're not very familiar with the layout and where you're at in relation, you'll be using up precious minutes getting your bearings.

This shouldn't be a problem, but if it is, don't worry - there are plenty of other ways to get from Narita in to Tokyo. The Skyliner goes direct to Ueno, and there are JR and Keisei lines which head into the city and take only half an hour longer than the N'EX and Skyliner.

See http://www.japan-guide.com/e/e2027.html

To be honest I think 45mins will not be enough. You can probably make it to the line at the customs, after that you'll have to claim your luggage, find your way down and line up again to buy your ticket.

I've been to Narita once before 2 years ago. I'm fairly good with my bearings and if it's doable with me making a bee line to everything I'll try.

I just want to catch the N'EX to take advantage of the N'EX + Suica package and I'm staying in Shinjuku.

It's cutting it very fine esp for buying a suica NEX.
If possible take your luggage as carry-on.