Updated 16:16 GMT
The United schemer clipped a superb lofted through ball to Shinji Okazaki after only four minutes allowing the striker to cheekily hook the ball home. Kagawa doubled the lead soon afterwards by rolling a penalty just out of the reach of Kiwi keeper Glen Moss.
Masato Morishige and Okazaki made it 4-0 with only 17 minutes gone but Chris Wood, who played against United at Under-21 level for Leicester City recently, restored some respectability to the scoreline with a brace.
Kagawa came off after 79 minutes with Manabu Saito taking his place and he will hope to return from the long trip to be considered for Saturday's early kick-off away to West Brom.
Afterwards, Kagawa revealed why he celebrated his penalty so enthusiastically. "A goal is a goal and I wanted to express my joy," he said. "We made a good start by scoring an early goal and I was happy to put away the penalty.