I came back and read this question again, and it occurred to me that maybe we should think of this a different way.
Perhaps H.G. Wells's 1897 novel The War of the Worlds will fit the bill.
Sure, there is no evil mastermind controlling the invading Martians, no linchpin individual whose removal makes the whole army collapse.
But the Martian invasion does in fact collapse suddenly and completely, and they all die, but not by any action of humans.
In another moment I had scrambled up the earthen rampart and stood upon its crest, and the interior of the redoubt was below me. A mighty space it was, with gigantic machines here and there within it, huge mounds of material and strange shelter places. And scattered about it, some in their overturned war-machines, some in the now rigid handling-machines, and a dozen of them stark and silent and laid in a row, were the Martians—dead!—slain by the putrefactive and disease bacteria against which their systems were unprepared; slain as the red weed was being slain; slain, after all man’s devices had failed, by the humblest things that God, in his wisdom, has put upon this earth.
TVTropes defines a Keystone Army as
an invasion force or army that's seemingly unstoppable, except for one particular weakness in the form of a well protected but very fragile component.
The Martians' weakness is their immune systems, which are admittedly not particularly well protected, but this occurred to neither the Martans nor Earthlings:
For so it had come about, as indeed I and many men might have foreseen had not terror and disaster blinded our minds. These germs of disease have taken toll of humanity since the beginning of things—taken toll of our prehuman ancestors since life began here. But by virtue of this natural selection of our kind we have developed resisting power; to no germs do we succumb without a struggle, and to many—those that cause putrefaction in dead matter, for instance—our living frames are altogether immune. But there are no bacteria in Mars, and directly these invaders arrived, directly they drank and fed, our microscopic allies began to work their overthrow. Already when I watched them they were irrevocably doomed, dying and rotting even as they went to and fro. It was inevitable. By the toll of a billion deaths man has bought his birthright of the earth, and it is his against all comers; it would still be his were the Martians ten times as mighty as they are. For neither do men live nor die in vain.
(Full text here)