We would consider three areas of influence to get at this question:
First, what author initiated a ground-breaking style that made all subsequent styles retreat to a historical period – in other words, who turned “modern” into “post-modern”? That would be James Joyce in prose (his Finnegan's Wake and Ulysses will enter the Great Books list for good), and T.S. Eliot in poetry (especially "Love Song of J. Alfred Prufrock".
Second, who opened the door to a new philosophical point of view? That would be Albert Camus's many existential novels (such as The Stranger) in prose (with Sartre's Being and Nothingness as the most influential nonfiction), and Samuel Beckett's Waiting for Godot and Endgame in drama.
Third, what 20th-century author will have the longest literary life in anthologies and reprints? That would be Ernest Hemingway (Farewell to Arms, and For Whom the Bell Tolls) in prose, and Robert Frost in poetry.
Of course, these are merely my assessments; others would see things another way.