Lee Carsley's youngsters will face either Germany or France, who meet later, in Saturday's final as they bid for a second straight title.
Liverpool midfielder Elliott hammered home the opening goal shortly after the hour mark, making up for two earlier missed chances.
But Dutch substitute Noah Ohio, who played for England at Under-16 level, equalised for the Netherlands in the 72nd minute with a speculative effort from long range.
Elliott, who was part of the England squad which won the tournament in 2023, had the final say with four minutes remaining, cutting inside and slotting a clinical finish into the bottom corner.
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