Mary and John were given the same task. In the end, Mary's work is better, and far exceeds his/him.
Is "him" grammatically incorrect here?
"him" would only be grammatically correct if your intention was to say that Mary's work exceeded John himself. As that likely isn't the case, you'd use "his" as the thing that Mary's work exceeds is John's work.
To put it another way, when talking about John's work in another context you wouldn't say something like "I really liked him work."
So to answer your question: yes, in this case "him" is incorrect.