By the end the German side had lost most of their discipline, though Rangers may regret not winning by a greater margin.
Goals either side of half-time by Daniel Cousin and Steven Davis were enough to give the home team a win, though both Rangers goals owed much to some shocking goalkeeping by Tim Wiese.
Cousin's speculative shot from 30 yards looked to be covered by the German keeper but he somehow he let it slip through his hands and then fumbled it into the net.
Wiese was also culpable for the second when he could only weakly palm out a Cousin strike, leaving Davis the simple task of taping the ball home from six yards.
Rangers made a bright start to the game with Charlie Adam's volley bringing a fine save from Wiese.
Bremen went close when Carlos Cuellar carelessly gave away possession and Allan McGregor had to be alert to palm away Markus Rosenberg powerful shot.
Adam provided most of Rangers' threat and his deflected free-kick troubled Wiese and then another free-kick from 30 yards went narrowly over.
Then came the two moments of disaster for the German keeper either side of half-time which left his team-mates shattered.
Davis went close to adding a third with a header from Barry Ferguson's cross, before Ferguson's shot went close.
McGregor made a fine save from Daniel Jensen's strike, before Rangers went so close to getting a third.
Lee McCulloch won a tussle between Naldo and Wiese after a high ball from Adam and, when the ball landed in front of the substitute from six yards out he looked only to have to tap home, but Naldo some how got his foot to it to turn it behind for a corner.