Two clinical goals from Sebastien Rudy and Zdravko Kuzmanovic on 16 and 59 minutes respectively proved enough but, in fairness, if it had not been for Allan McGregor’s heroics it could have been more.
Kris Boyd made his first Champions League start as Walter Smith’s men chased the three points they required to keep their qualification hopes alive.
The striker, of course, has been in excellent form recently and five goals in his last four games convinced the manager that he deserved his chance.
The other big news for Gers fans ahead of kick-off was that Madjid Bougherra, as expected, has not been selected in the first XI.
The Algerian was named on the bench meaning young Danny Wilson was alongside David Weir and the youngster was faultless on the night.
The team only had one change in it from the 3-0 weekend win over Kilmarnock and that was an enforced one, with Lafferty taking the injured Steven Naismith’s place.
In the early stages Stuttgart showed their quality, as they did in Germany on matchday 1, and Rangers looked nervous despite being on home turf.
Marcus Babbel’s men looked sharp and confident despite their 16th place position in the Bundesliga and almost straight away McGregor had to be on his toes.
With Rangers pegged back Cacau made space for himself with a neat turn but his right foot curler from 20 yards was brilliantly palmed away by the keeper.
This was a sign of things to come and when the deadlock was finally broken it did not come as a surprise.
Aleksandr Hleb played a neat one two on the left and although his cut back was missed by Pavel Pogrebnyak midfielder Rudy was there to drill the ball home from five yards.
The goal prompted Walter Smith to move from his Directors Box seat in to the dug-out and he immediately changed his strategy back to a traditional 4-4-2 with Miller joining Boyd in attack.
This, however, did little initially with Rangers struggling to get on the ball and a bit of frustration crept in.
On 25 minutes Kevin Thomson was guilty of a poor challenge on Ricardo Osorio, his second of the night, and referee Roberto Rosetti had no option but to produce the first yellow card of the game.
On the half-hour mark there were signs that the Light Blues were settling and a rasping left foot shot from Boyd had Lehmann scrambling across goal but the ball went narrowly wide.
On 37 minutes Kenny Miller then found space on the right wing and his delightful cross was headed over by Boyd from eight yards. The striker had his hands on his heads and by his standards it was a sitter.
Smith would certainly have been happier with the way his side finished the first-half and it gave the Ibrox faithful a bit of hope for the second period although the news that Unirea were beating Sevilla at half-time was a shocker.
With McCulloch and Thomson both booked in the in the first-half a bit focus would be required in the second from the midfield duo – especially on a treacherous surface.
Rangers, however, started the second-half positively but the threat from players such as Hleb, Rudy and Cacua meant that switching off for a second would be fatal as this unfortunately proved.
On 55 minutes, however, Rangers gave the Germans a fright when Steven Davis slid the ball past the static defence to Miller but the lineman had already signalled for offside before his cut back reach Boyd who would have tapped the ball in to the net.
A pivotal point in the match then came on 58 minutes. Kenny Miller was played through on goal by Davis but rock solid stopper Matthieu Delpierre did brilliantly to get back and produce a last ditch challenge.
In the very next attack the ball was played out wide to Rudy on the right and when his cross was missed by Weir Zdravko Kuzmanovic headed powerfully beyond the helpless McGregor.
Things could have got even worse for Rangers two minutes later when Rudy darted 30 yards down the right wing before cutting it back intelligently to Cacau 30 yards out.
His shot took a deflection on the way through and when McGregor’s block with his legs came back out to Pogrebnyak the keeper made a miraculous stop to deny the former Zenit hitman.
After comfortably beating Killie at Ibrox on Saturday Rangers were now struggling to cope with the Germans who were picking their passes and looking dangerous with every attack.
With time running out and nothing to lose Nacho Novo was introduced on 67 minutes in place of Miller.
So often an impact player from the bench it was not to be on this occasion for the Spaniard who could do little to help his side in the time remaining.
At the other end Stuttgart continued to threaten and luck was on Rangers’ side when Pogrebnyak smashed the ball off the post on the turn from a tight angle.
And in the last five minutes McGregor has to be at his very best to deny substitutes Julian Schieber and then Timo Gebhart with only seconds left on the clock.
In the end this was a desperately disappointing night for the Light Blues but teenage star Wilson can again hold his head high while McGregor showed once again that there are few keepers better in European football on this form.