And, with the team sitting second in the Bundesliga looking far from world-beaters, Rangers must fancy their chances of reaching the last eight stage of the tournament.
Rangers came close to the perfect opening but Wiese was at full stretch inside the first minute to push away a thumping long range strike from Charlie Adam.
However, the home side could not build on their bright start, with both teams packing men behind the ball and struggling to establish any passing momentum.
A stray pass from Rangers defender Carlos Cuellar gave Markus Rosenberg a glimpse of goal on 21 minutes but Allan McGregor made a great diving save to stop the striker's 25-yard shot.
A deflected free-kick from Adam missed the head of Barry Ferguson by inches and no other Rangers player could take advantage of an unconvincing punch clear by Wiese.
Adam again threatened from distance when his impressive 35-yard free-kick curled on to the roof of Wiese's net.
Cousin had endured a frustrating first 45 minutes, seeing very little of the ball, but his speculative long range effort fired Rangers in front on the stroke of half time.
The French forward let fly from fully 35 yards after cutting in from the left flank and Wiese made a terrible blunder, simply pushing the ball up in the air and into his own net to give the home fans an unexpected treat.
Davis capped a fine performance with the second goal
Wiese's generous mood continued after the interval and Rangers doubled their lead on 47 minutes thanks to another mistake from the keeper.
Cousin drilled in an angled strike from the edge of the penalty area and it squirmed from Wiese's grasp, allowing Davis to slide the loose ball into an empty net.
Davis and Ferguson were causing the visitors problems with their runs from midfield and the Northern Ireland international sent a dangerous header over the crossbar from 10 yards.
The Scotland skipper then smashed a shot narrowly wide, with the German defence backing off.
McGregor had to deal with a skidding strike from Daniel Jensen before McCulloch squandered a wonderful chance to extend Rangers' advantage.
With 87 minutes on the clock, the substitute latched on to a bad headed back-pass from Naldo and knocked the ball under the advancing Wiese, only to allow the defender to make a recovering tackle almost under the crossbar.
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