My background is in NURBs modeling and Maya's implementation is very weak. NURB's have not been updated in Maya for more then 10 years!

However capping a non-planar opening, even in more up to date and sophisticated NURBs modeling apps like Rhino, Inventor, and SolidWorks can be a complicated task.

Especially if you want to manipulate the cap dynamically. There are approaches using booleans that could work where you use another surface as a cutter. In Maya after you apply the boolean the cutter is not longer visible but it is still there and with history and can be manipulated.

I think I recorded a video a while back on this approach although as I recall it was for polygons and was pretty simple (just to demonstrate the concept). But it should translate to NURBs if you require using them for your project.

Maya would not be my first choice for building a full on NURBs model though.

I will check to see if I can find a link to the video for you.