New signing Kagawa, who was named as man of the match, found the net after 68 minutes against a second-string Shenhua outfit, who lined up without former Chelsea players Nicolas Anelka and Didier Drogba at the Shanghai Stadium.
United dominated for long periods and were rewarded when the Japanese international found the back of the net with a deflected effort after being set-up by Bebe.
United boss Sir Alex Ferguson tells MUTV: "I was very pleased with the way we played very well in the second half.
"In the first half we had a lot of possession but lacked penetration and speed of play. It's been a great workout, they were very well organised. They weren't easy to play against."