How to make older iPhone and iPad with < iOS 8 enter two factor verification code?

I have some older iPhone and iPad (iPhone 5S and iPad Mini) with iOS 8. When I charged it and powered it up again, and search for app in the App Store, it will ask me to verify the account in my other apple device.

Sure, my iPhone 6 Plus and Macbook both popped up the "Allow or not" and verification code popups, but in the older device, there is no way to type the code in.

If I don't create yet another iTunes account (and want to use the existing iTunes account), and not to be forced into upgrading to the newest iOS, how can I possibly make it work?

This stumped me for several attempts, until I carefully re-read the pop-up window with the verification code (I didn't take a screenshot, I'm going from memory):

enter the verification code after the password INTO THE PASSWORD field (my CAPS)

So, there is no separate box or window for the verification code. You have to type both the password and code into the same box as one long string.

This worked for me in iOS 5.1

Looks like a way to retro-fit 2-factor into iOS5 without having to release an update.