Davis sealed the win early in the second half after Daniel Cousin put his failed move to Fulham firmly behind him with a goal on the stroke of half-time.

The last time Rangers treated their fans to European goals at home was against Stuttgart here back in September and Walter Smith's men were on top form against German opposition again to improve their chances of seeing out the tie in Bremen next week.

Cousin was deployed as the lone striker in the absence of Jean-Claude Darcheville, who was serving the last of a three-match European ban.

Brahim Hemdani was drafted into the midfield to provide stability alongside Christian Dailly, allowing Barry Ferguson to play further forward, while Sasa Papac was given the nod ahead of Steven Whittaker at left-back.

Charlie Adam held onto his place in the team at the expense of Lee McCulloch and made the most of the opportunity.

Boosted by his goal against Aberdeen at the weekend, he had a shot in the opening minute and drew a superb save from goalkeeper Tim Wiese with a powerful drive from the edge of the box.

The midfielder then tried his luck again with an audacious lob from a yard inside the opposition half after spotting Wiese well off his line but, fortunately for Bremen, he was just off target.

The Germans also managed a few ventures forward and Markus Rosenberg clearly fancied his chances after bagging a double against Borussia Dortmund at the weekend.

His long-ranger was well-struck but Rangers goalkeeper Allan McGregor did well to palm to safety and keep the scoreline level.

A couple of free-kicks allowed Rangers to pile on the pressure at the other end.

Adam delivered an inviting ball into the packed goalmouth and Barry Ferguson got a touch in front of goal.

But the Rangers skipper failed to mark his record-breaking 77th European appearance with a goal when Wiese produced a point-blank save.

Another set-piece from Adam, this time from 25 yards, screamed inches over the crossbar and landed on the roof of the net, with Wiese looking well-beaten this time.

Bremen could have snatched the opener when McGregor was called upon to dive low to the far post to smother Jurica Vranjes' header from a Diego corner.

But Rangers took the lead on the stroke of half-time in stunning style.

Wiese managed to get both hands to the ball but Cousin's sublime, 35-yard shot was packed with so much power that the Bremen goalkeeper succeeded only in helping the ball drift over his head and into the net.

Just when the Ibrox faithful thought their night could not get any better, it did.

Davis started the move when he released Cousin out on the right flank and the striker's angled drive was parried by Wiese. The keeper was left with no chance when Davis followed up to rifle home the rebound from six yards just two minutes after the restart.

The on-loan Fulham midfielder could then have grabbed his second of the night when Ferguson whipped a cross in from the left and a full-stretch Davis saw his header dip just over the crossbar.

Ferguson then saw a long-range shot deflected wide as Rangers cranked up the pressure.

Cousin signalled to the bench that he was struggling and was withdrawn for McCulloch for the last 15 minutes.

McCulloch should have added his name to the scoresheet when he beat the keeper and bore down on goal only to somehow be denied by a superb last-gasp tackle from Naldo.

Rangers held on for what proved to be a comfortable win and will now head to Germany full of confidence for the second leg on March 13.