The 23-year-old midfielder, who is set to become United’s first signing of the summer, swept home his country’s fourth goal 10 minutes before the break in Saitama.
CSKA Moscow’s Keisuke Honda bagged a hat-trick, with Ryoichi Maeda and Yuzo Kurihara also on target, as the Samurai Blue eased to two wins from two in Group B.
Kagawa again opted not to talk about his transfer after the game, instead focusing on Japan’s next match, a tougher assignment against Australia in Brisbane on Tuesday.
"It was good to win so well, even if my goal came about through a Jordan mistake," he said. "Our next game will be tough, but we will just try to do what it takes to win."