You have discovered
subject-auxiliary inversion, specifically
negative inversion. SAI occurs most frequently in questions, but it also occurs after negative phrases and clauses, with some uses of the subjunctive ("Had I known . . .") and in some clauses with
than,
as, or
so ("so did Bob"). In this case, the
only clause is negative because it essentially means "in no case except this one".
Explaining that such phrases cause inversion is easier than explaining why. It's apparently an ongoing problem in theories of syntax. But the constructions is apparently a holdover from earlier English syntax (known by linguists as V2, because the verb is always the second constituent in the sentence) that is still alive and well in other Germanic languages. In V2 languages, the nominal word order is subject-verb-object, but you can bump the subject from its slot but putting another constituent in its place, whether an adverb, object, or some other kind of complement. The verb stays put, and the subject moves after it. You can still see it sometimes in Early Modern English, but today it only appears (outside of questions) in a limited range of constructions, and it now requires creating an auxiliary verb if there isn't one ("I never kicked puppies" > "Never did I kick puppies").
P.S.: I'd also take out the comma after the fronted negative clause, but I'm having a hard time explaining why it would need it in your original but not in the revised sentence.