Kagawa, who was later named man of the match, blasted home via a deflection on 68 minutes to hand Sir Alex's men victory in the Reds' only Asian pre-season fixture of the DHL 2012 Tour.
Despite the win, the Reds struggled in Shanghai's heat and humidity to play at pace and again looked disjointed for long periods.
Shanghai Shenhua, without former Chelsea stars Didier Drogba or Nicolas Anelka (neither was named in the matchday squad), didn't help matters, mind you. The home side effectively parked the bus for 90 minutes, getting men behind the ball at every opportunity and threatening only on the counter-attack.
In Drogba and Anelka's absence it was left to Joel Griffiths and Song Yan to lead the line for the Chinese outfit against an unfamiliar Reds defence.
Rio Ferdinand started at its heart, with Michael Carrick, more accustomed to a midfield role, alongside him. Frederic Veseli and Robbie Brady patrolled the flanks, just as they did in United's pre-season opener in Durban last week.
Yan had the first shot of the game when he was afforded space to shoot from 20 yards. But it was a tame effort, easily fielded by Anders Lindegaard.
Sir Alex handed summer signing Nick Powell his first start in a United shirt but it was a debut that got off to a bad start when he was caught by a