Allan McGregor was the Rangers hero as Walter Smith's team rode their luck in Bremen to reach the Uefa Cup quarter-finals.
His Werder Bremen counterpart Tim Wiese was the German team's culprit in the tie – his two calamitous mistakes at Ibrox last week proving decisive over the 180 minutes.
The visitors to the Weserstadion last night had to withstand a major onslaught from the hosts who took the lead in the 58th minute thanks to a sublime goal from Diego.
Werder almost struck through Boubacar Sanogo five minutes from time, but goalkeeper McGregor touched the close-range shot against the bar.
Bremen asserted themselves throughout the first 45 minutes, with McGregor excelling in particular to save from Daniel Jensen and turn Patrick Owomoyela's effort past the post.
There was no let-up after the interval as Bremen launched one furious assault after another, and Diego finally made the breakthrough shortly before the hour. The Brazilian made space for himself with some superb skill on the edge of the penalty area and then beat McGregor with a low shot across the goalkeeper and into the right corner.
The best chance to take the game to extra time fell to the substitute Sanogo, six yards out, but McGregor somehow managed to tip his effort on to the bar. Bremen would not come so close again and Rangers held out to progress.
Werder Bremen (4-4-2): Wiese; Owomoyela (Harnik, 78), Mertesacker, Naldo, Boenisch; Jensen, Borowski, Hunt, Diego; Rosenberg, Hugo Almeida (Sanogo, 66). Substitutes not used: Vander, Vranjes, Ozil, Tosic.
Rangers (4-4-2): McGregor; Broadfoot, Weir, Cuellar, Papac; Hemdani, Dailly, Ferguson, Davis; Adam (Whittaker, 57), Novo (McCulloch, 78). Substitutes not used: Alexander, Buffel, Thomson, Boyd, Naismith.
Referee: M Hansson (Sweden).
Uefa Cup last eight
Bayern Munich, Zenit St Petersburg, Bayer Leverkusen, Fiorentina, PSV Eindhoven, Getafe, Rangers, Sporting Lisbon
Quarter-finals 3/10 April. Draw today