United had already established superiority thanks to first-half headers from Nemanja Vidic and Cristiano Ronaldo.
The Japanese briefly brought themselves back into the match, when Masato Yamazaki made it 2-1, only for Rooney to finish low into the far corner seconds later.
They were trailing 5-1, before a Yasuhito Endo penalty and Hideo Hashimoto made the scoreline more respectable.
United's final opponents LDU Quito defeated Mexico's Pachuca 2-0 on Wednesday in the other semi-final.
