The Red Devils took the lead on 17 minutes through Wayne Rooney's thumping finish.
Shoddy defending allowed Inter back into the game as David Suazo scored from close range after Luis Figo's cross was not cleared.
A sweeping move from Inter saw Zlatan Ibrahimovic put the Serie A side in front on 27 minutes before Suazo scored his second of the night on 34 minutes.
Adriano headed Cristiano Ronaldo's free-kick into his own net in the second half before Rio Ferdinand missed a gilt-edged opportunity to equalise.