Bremen were forced into a change midway through a tight first half as Eljero Elia pulled up with an injury, forcing the visitors to bring on Franco di Santo after 30 minutes.
Mielitz was then culpable as Gladbach doubled their advantage early in the second half, with Raffael the man to benefit as he reacted quickest to a spilled spot to find the target.
Bremen had two strong penalty claims turned down as they looked to quickly reduce the deficit, which they did 20 minutes from time as Havard Nordveit got the final touch to turn into his own net.
Any hopes of a comeback for the visitors lasted just four minutes as Max Kruse finished a fine counter at the other end, restoring Gladbach's two-goal advantage.
Kruse then combined with Patrick Herrmann to put the result beyond doubt five minutes from time, ensuring Gladbach earned a 4-1 win to savour.