Include unrelated patent on publication list
Yes, you should list it. Even if you had an otherwise rich CV it would still be proper to list it. 

Your application needs to make your best case for acceptance and any IP contributions show evidence of quality research. People understand that patents are hard to obtain. 

Your application otherwise will show mostly work in progress, which is fine, but work completed is also a good indicator. You might want to explain your change of fields if that is relevant also, or, at least be prepared to discuss it.