Inadvertently
Part of speech: adverb
Definition: Unintentionally, because of an oversight.
Example sentence: America's strength has made it a sort of Gulliver in world affairs: By wiggling its toes it can, often inadvertently, break the arm of a Lilliputian.
Unwittingly
Part of speech: adverb
Definition: In an unwitting manner; inadvertently, unintentionally, unknowingly.