Associating Products from Deal to Account

Associating Products from Deal to Account

I've searched for an answer to this, but only found an old post from 6 years ago that said it was not possible. We have an API writing to Deals anytime our internal order entry tool closes a deal. It writes to the CRM with the products that were purchased by our customer. What I am trying to accomplish is also having those products tied to the account. I know we can probably do this using the API, but was wondering if there is a way to accomplish this otherwise. 

Basically, if a deal closes with Product A, we want Product A to show up in the Products Module on the account.