Rangers, wearing all blue once again, made three changes from the side which had struggled to beat Aberdeen at the weekend with Maurice Ross, Zurab Khizanishvili, and Nuno Capucho replacing Emerson, Arteta and Mols.
There was a familiar face in the shape of Spanish Manuel Gonzalez who had taken charge of the 1-1 draw with FC Copenhagen earlier this season.
The home side made a lightening start with Alexander Hleb breaking free on the right, his cross being turned behind by Henning Berg.
Rangers settled to their game, but were under increasing pressure - Phillipp Lahm 12th minute free kick from a wide angle flashing across the face of goal.
Six minutes laster as Rangers started to push up, a Paolo Vanoli error in the opposition half enabled the Germs to break swiftly - Hleb breaking free and running half the length of the park before being stopped in his tracks by the retreating Stephen Hughes.
Rangers were now starting to impose themselves on the game, having perhaps having started too cautiously, and a golden chance as spurned in 22 minutes when a Ross cross was chested on by Shota Arveladze into the path of the unmarked Fernando Ricksen whose left foot shot was deflected wide by goalkeeper Timo Hildebrand.
Two minutes later Kevin Kuranyi spurned and equally good opportunity at the other end when he shot wide from a Hleb pass.
Rangers continued to allow Stuttgart too much space on the flanks (and too much respect) - underlined on the half hour when Lahm, in acres of space, saw his volley from a Hleb free kick held by Stefan Klos.
It was Klos to the rescue shortly afterwards, denying Kuranyi at point blank range from Silvio Meissner’s opening.
As the first half drew to a close Rangers were comfortable, composed, and gaining in confidence - yet right on the interval Stuttgart snatched the opening goal in the most controversial of circumstances following the award of an extremely soft free kick against Khizanishvili.
Horst Heldt’s lob into the box saw the ball break between Ross and Vanoli, falling perfectly for Timo Wenzel who volleyed a left foot shot into the net.
There was little justice in Rangers trailing at the interval but the job in hand was now twice as difficult.
To many people’s surprise manager Alex McLeish started with the same eleven in the second half despite the apparent ineffectiveness of both Capucho and Vanoli.
The Scottish champions enjoyed the greater share of possession throughout most of the second half without greatly threatening the Stuttgart goal. The introduction of Michael Mols and Egil Østenstad for Vanoli and Ross indicated that Alex McLeish knew he needed a greater presence up front, but it was Stuttgart who remained dangerous on the counter attack - Christian Tiffert firing a low drive just wide from a Hleb break on the hour.
Chris Burke replaced Lovenkrands for the last ten minutes in last throw of the dice - but not even the youngsters pace could effect a breakthrough.
The final whistle brought joy to the home fans but for Rangers the task is now a simple on - to ensure Panathanikos do not win at Ibrox and thus gain entry into the UEFA Cup.
Manager Alex McLeish said afterwards “I could not complain about the effort, the players gave me everything. It was a bad goal to lose. The application and work rate tonight was so much better than at Old Trafford. We restricted Stuttgart to few chances. However you need to have all your best players available to compete at this level.”
Stuttgart coach Felix Magath was more than satisfied with his teams performance “I was happy with my teams play, Stuttgart’s success if down to a team success by everyone.”
However, the Stuttgart coach also directed a thinly-veiled jibe at Celtic when he added - “The Stuttgart fairy tale has been ongoing for two years now. Last year we finished second in the Bundesliga and must have reached the UEFA Cup Final had we received as fair a share of the refereeing decisions in our game in Glasgow as Bayern Munich did last night.”
Stuttgart
1 Hildebrand
2 Hinkel
3 Wenzel
6 Fernando Meira
7 Meissner
15 Hleb (Centurión 73)
16 Heldt (Tiffert 49)
19 Szabics
20 Soldo
21 Lahm
22 Kuranyi
SUBS
23 Heinen
11 Amanatidis
12 Gerber
18 Cacau
35 Branco
Rangers
1 Klos
2 Ricksen
7 Shota Arveladze
15 Khizanishvili
16 Vanoli (Mols 55)
18 Ball
20 Capucho
21 Ross (Østenstad 70)
25 Berg
26 Lovenkrands
27 Hughes
SUBS
22 McGregor
4 Emerson
30 Burke
33 Gibson
42 Steven Smith