The Black Cats made it four wins out of five friendlies in Denmark, with new signing Jozy Altidore setting up the former Manchester City man for the only goal of the game
Adam Johnson grabbed his first goal of pre-season courtesy of an assist from new arrival Jozy Altidore in the first half, though Paolo Di Canio's men failed to add to their tally despite dominating the second period.
However, the Italian is still likely to be pleased with his side's efforts in their final fixture ahead of an opening-day Premier League clash with Fulham.
FC Midtjylland came into the game having already played three domestic fixtures but, despite making an encouraging start to proceedings that seemed to hint at their greater sharpness, they were soon behind
Altidore, whose fine goalscoring record has been regularly referenced since his switch from AZ Alkmaar, evidenced another side of his game as he teed up Johnson to curl a trademark effort in at the far post.
The hosts almost summoned a response not long after, as Keiren Westwood needed to be on his toes to keep out a Frank Kristensen effort.
But Sunderland looked the most likely to get another before the break, as Sebastian Larsson and Emanuele Giaccherini both went close.
The second period saw a host of changes - including an incredible eight in one go from FC Midtjylland - and both teams struggled to get going as a result.
A well-saved Stephane Sessegnon attempt was in truth as near as either side came, and Sunderland were rarely threatened as they saw out a fourth victory in five pre-season games.