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David Melvin reporting from the Gottlieb Daimler Stadium
RANGERS need only a draw against Lyon at Ibrox in the final match of Group E after a 3-2 defeat in Stuttgart left them second in the table.
With Lyon and Barcelona finishing level in France, Walter Smith's side go into the final game level on points with the French side.
Rangers' 3-0 win in Lyon means a draw will leave them with a better head-to-head record against the French.
A late goal from Ciprian Marica gave the German side their first points of them campaign and meant qualification for the last 16 will come down to the crucial Ibrox clash on December 12.
In an open early period Rangers had two good chances in the first ten minutes with Beasley failing to get his shot off inside the box after Barry Ferguson's shot ricocheted into his path after just six minutes.
Four minutes later Jean Claude Darcheville latched on to a Lee McCulloch pass but fired his shot past the near post into the side netting.
Stuttgart responded well and Rangers had Allan McGregor to thank for a series of saves that kept them in the match.
The pick of the bunch came in the 18th minute when he blocked with his feet after Cacau found himself clean through.
Rangers broke well and Darcheville's square ball found Kevin Thomson and the midfielder's left foot shot was well blocked by Matthieu Delpierre.
From the resulting corner, Ferguson found Davie Weir and the Scotland defender's header was stopped at the post by Ludovic Magnin.
Walter Smith was then forced to make the first of two replacements due to injury. McCulloch was penalised for a foul on Pavel Pardo but injured himself as he tried to win the ball back from Andreas Beck.
McCulloch was booked for the first challenge as he trudged off the pitch to be replaced by Charlie Adam.
And it was the man who scored the first goal against Stuttgart at Ibrox on matchday one, that again found the net just 59 seconds later.
Adam scored with his first touch when was on hand to sweep the ball home from Carlos Cuellar's knock down after a pinpoint corner from DaMarcus Beasley.
McGregor was again called upon to make some important stops as Stuttgart looked to get back into the game quickly.
Rangers continued to play on the break and Beasley was pulled down by Magnin as he sprinted down the right hand side, the Swiss defender picking up a yellow card for the challenge.
With Stuttgart continuing to look dangerous, Thomas Hitzlsperger's floated cross found Sami Khedira seven yards out, but the 20-year-old playmaker could only scoop his effort over the bar on the stretch.
As Rangers looked set to go in with a 1-0 lead a poorly defended corner allowed Pardo to fire in an effort from the edge of the box and Cacau's flick was enough to beat McGregor and level the scores deep into first half injury time.
Smith was forced into a second change shortly after the break when Beasley came off worst when Raphael Schafer smothered his shot after 
Darcheville had slipped him in behind the Stuttgart defence.
Steven Naismith was introduced to replace the American international, but it was Stuttgart who continued to look threatening on their right hand side.
Cacau's low cross in the 58th minute rolled along the six yard line, but there were no takers for Stuttgart.
The home side's breakthrough did come just four minutes later when Pardo's 25 yard drive slipped under McGregor and nestled in the bottom corner of his net.
It took Gers just eight minutes to get back on level terms when Naismith found himself free on the right and his low cross was pushed out by Schafer to Ferguson.
With the keeper helpless, the captain composed himself and rolled the ball in from six yards to bring the sides level.
Ferguson almost turned provider two minutes later with a carbon copy cross that just eluded Adam as he went looking for his second.
With Lyon drawing at home to Barcelona qualification was within Rangers' grasp, but it was Stuttgart who found the third goal.
Magnin's flighted cross from the left found Ciprian Marica in space in the Rangers box and a flick of his right foot directed the ball over McGregor and into the top of the net with five minutes left.
Rangers: McGregor; Hutton, Cuellar, Weir, Papac; Beasley (Naismith 47), Thomson, Hemdani, Ferguson, McCulloch (Adam 25); Darcheville (Cousin 81).
Subs: Carroll, Broadfoot, Whittaker, Boyd.
Booked: McCulloch, Adam, Hutton
Stuttgart: Schafer; Beck, Fernando Meira, Delpierre, Magnin; Hilbert (Ewerthon 82), Pardo, Khedira (Antonio Da Silva 46), Hitzlsperger; Marica, Cacau (Tasci 87).
Subs: Langer, Osoria, Meissner, Farnerud.
Booked: Magnin
Referee: Darko Ceferin (Slovenia)
