Invocation spells are Warlock spells for you and they benefit from Rod of the Pact Keeper.
By omission, the rules for invocation spells like confusion use your Warlock spell save DC. If that were not so, the class would mention what spell save DC to use instead. The rules as written define a spell save DC only once in the Warlock class: your Warlock spell save DC. So that's the one you use when you cast a spell through a Warlock feature requiring a saving throw. Nothing in the Warlock rules would suggest otherwise.
Regardless of what list a spell appears on, if a class feature tells you that you can cast a spell and the only way you can cast that spell is because you have that feature, then it's a class spell for you: literally, it is a spell based upon your class. By contrast, a spell you can only cast because you're a multiclass Sorcerer or because you're a Drow would not be a Warlock spell for you. So when you cast confusion using your invocation, you're casting one of your Warlock spells.
Therefore, yes, you benefit from Rod of the Pact Keeper's bonus to spell save DC when you cast confusion using an invocation. This reading is the simplest and most obvious.
Within the text of the Warlock class, the most straightforward and literal reading is that any spell it grants you is a Warlock spell for you, whether or not a particular shibboleth phrase declares that it is. Otherwise, if the term "class spell" were intended to be so rigorous and unintuitive as to exclude spells you can cast through your own class, we'd expect the term to be defined somewhere in the rules. It's not, so the rules as written default to the plain English meaning of the words. It's rules as written, not rules as legalistic.
Nevertheless, knowing the design intent doesn't hurt. The lead rules designer of 5e, Jeremy Crawford, confirmed this intention when I asked him about it on Twitter:
Me: If I am a Warlock and I use an invocation to cast a spell that's not on the Warlock list (such as Levitate, Confusion, or Slow) requiring a save, does it use my Warlock spell save DC? Also, can such a spell benefit from Rod of the Pact Keeper?
Crawford: The spells you cast through the Eldritch Invocations feature are meant to be warlock spells for you.
Crawford's tweets are not rules as written and are merely indicative of the design intent, but in this case it matches the simplest reading of the text.