Former Zenit striker Pavel Pogrebnyak gave the home side the lead with a well taken strike after 18 minutes and it was no more than they deserved at that stage.
But Rangers were a different side after the interval and almost nicked a win at the death when Steven Davis saw his low left-foot shot clip the post.
In a game which looked lost Rangers somehow fought their way back in and the goal sent the 2500 Bears in the Mercedes Benz Arena in to ecstasy.
Prior to the game Walter Smith suffered a blow with the news that captain David Weir was unavailable due to injury.
The 39-year-old has bruising to his ankle following an incident in Saturday’s 0-0 draw at Fir Park.
His absence meant that Lee McCulloch partnered Bougherra in the heart of defence with Steven Whittaker and Sasa Papac at right and left back respectively.
As expected Smith has elected to use his favoured 4-1-4-1 Euro formation with Kevin Thomson returning to the starting eleven in a holding midfield role.
Steven Naismith was also back in the team on the left wing with Rothen on the right.
In the centre Steven Davis joined Champions League winner Pedro Mendes and the big news for the home side was that Aleksandr Hleb made the game having recovered from a back injury.
Backed by a vocal home support Stuttgart started the match in some style with their skill and movement carving out several goalscoring opportunities.
After only 30 seconds Allan McGregor was called in to action when right winger Roberto Hilbert cut the ball back to Cacau beautifully and his first-time shot was well saved by the keeper who dived to his left to palm it out.
The rebound fell to Pobrebnyak but his acrobatic volley from eight yards was well over.
At the other end Mendes tested Jens Lehmann with a 25 yard shot but the former Arsenal man was up to task.
In the early exchanges Rangers were struggling to deal with Stuttgart’s direct approach and McGregor again had to be lively to touch a near post cross come shot from Hleb around his post before Cacau blasted an effort over the bar.
The warning signs were there but the manner in which Rangers conceded the first goal infuriated Walter Smith.
Papac was robbed of possession on the halfway line after appearing to slip and from there Stuttgart had three men pushing forward with only Bougherra standing in their way.
Cacau laid it on a plate for his strike partner Pogrebnyak who fired it low in to the net from the penalty spot.
No one could deny that Marcus Babbel’s men deserved to get their noses in front but following the goal Rangers started to enjoy a bit more possession although clear cut chances were few and far between.
The best came the way of Naismith with 30 minutes on the clock.
Rothen swerved a delightful pass through to the onrushing striker who was bearing down on goal but Naisy’s first touch deserted him and the ball ran harmlessly out of play.
This summed up Rangers’ first-half and the management team must have been relieved to hear referee Massimo Busacca’s half-time whistle.
The 1-0 scoreline meant the Light Blues were still in the game when, in truth, they shouldn’t have been.
But the start of the second-half provided a bit of hope.
Rothen was again the arcthitect when he cut inside from his right berth before delivering a teasing cross in to the box.
It fell to Papac at the back post but the Bosnian headed wide from just six yards.
Rangers were all of a sudden looking more positive with Miller looking more comfortable in possession and allowing the midfield to push further up the pitch.
Rothen was showing glimpses of his undoubted quality and he was close to bring his side back on level terms on 63 minutes.
The on-loan Frenchman’s attempted cross with his right-foot almost deceived Lehmann who could only watch on as the ball clattered his near post.
Rangers were now in the ascendancy but this was not to be one of Papac’s better nights and he received the first booking of the night when he attempted an overhead kick in the box but booted Christian Trasch in the face.
Lehmann darted from his line to confront the left-back who was understandably annoyed at the German’s over-the-top reaction.
Rothen’s second-half display was a highlight on the night and with 15 minutes remaining he swung in a wicked corner which was missed by both Whittaker and McCulloch who were in acres of space.
If Stuttgart were the dominant side in the first-half Rangers were now on top and they got their reward on 76 minutes.
Bougherra played a clever one-two Steven Davis 20 yards from goal and Algerian’s rocket shot from a wide angle gave Lehmann no chance at his near post.
It was a goal a striker would have been proud of and from there the visitors went in search of a winner.
On 83 minutes it almost came from the impressive Naismith who ran his socks off all night for the cause.
After a free-kick from Hitzlsperger hit the Gers’ wall a sea of Light Blue jerseys pushed forward and Miller played a great pass through to Naisy.
His touch in to the box was poor but he then tackled Arthur Boka brilliantly to get it back.
All that was left was to beat Lehmann but the giant keeper narrowed the angle before producing an excellent stop.
At the other end Pogrebnyak had a late chance to net a winner with a 20 yard free-kick but his effort again hit the defensive wall.
In what was a dramatic end to the 90 minutes Rangers were inches away from snatching what would have been a remarkable win.
Davis had his head in his hands when he saw a low left foot shot from 18 yards clip the outside of Lehmann’s right hand post.
Regardless, this was a night to be proud of for Rangers who showed great courage to earn a stunning point.