I think that the best example of "destruction by otherness" in Lovecraft is "The Color Out of Space" (a tale that terrified me when I was a kid, and for all good reasons). It was Lovecraft's favourite among his own works, and his attempt to "finally describe a truly alien entity" (an intent that gives a strange context to the rest of his creations...)
In the story, a "Color not from this Earth" mercilessly destroys a family of innocent, hard working farmers. The story has a strange structure: it is told to us by an unnamed character who hears it from an old farmer, young when the facts happened; this farmer, in turn, got fragments of these events from the victims, thus creating an almost clinical detachment from us to the "strange days" when the Color came to Earth.
IMHO, Lovecraft succeeded in his objective, showing us sheer... "evil"? permeating the earth, the bodies of any living thing in the stricken area, and ultimately the minds of the innocent victims. There is no "screaming realisation at the end", fade to black (well, a bit). Nothing is spared to them (and to us): the utter devastation is almost told "live", with a sort of unblinking stare uncommon for Lovecraft.
And yet, we are told "It was just a Color", only to be reminded "A Color out of space." If you don't look for them, they will come for you anyway. Was it an accident? Was this entity even intelligent? Can we really speak of "intelligence" (or "evilness") thinking that the word has for "it" the same meaning that it has for us? For all the detail that Lovecraft puts in this story, we are not told. It happened, pray that it will not happen to you.
To me TCOoS is the "ultimate Lovecraft". He doesn't need bad seafood or mercifully lost cities to make his point. It is something not even hidden to the World: the Color is unbothered by acting in plain sight, it the presence of common people, scientists and policemen. You can imprison or kill a Deep One, or cause a setback to Cthulhu itself, but here there is, literally, nothing we can go against: it is not even a form of energy (that we can understand at least). It is a Color.
This story does seem to be "isolated" by the rest of the Mythos, almost stand-alone (except for the fact that it is set in the hinterlands of Arkham) - but there is a totally throwaway reference to the Color at the end of "At the Mountains of Madness". If, by then, Lovecraft was having fun at throwing the kitchen sink into his "magnum opus" or if he had plans to clarify the reference that were cut short by his untimely death, I guess we will never know.