To buy a specific fare class, or to know in advance which fare class the ticket you are about to purchase is in, then you MUST use a website (such as Expedia, for example) that shows you in advance which fare class the ticket you have selected is in.

You cannot look up a ticket on one website (itasoftware) and buy a ticket on a separate website (UX.com) and have any guarantee that the tickets will both be identical