The Light Blues' third home defeat in the section leaves them at the bottom of Group G with just two points and a meaningless trip to Sevilla next month to conclude their fixtures.
Stuttgart may be struggling in 16th place in the Bundesliga but they needed just 16 minutes to take the lead, Rudy sliding the ball in from 12 yards after being set up by Aleksandr Hleb, who had lost defender Steven Whittaker inside the home penalty area.
The second goal in the 58th minute, when Kuzmanovic headed Rudy's cross past the helpless Allan McGregor, effectively ended the tie and indeed, if it had not been for the good form of the Rangers goalkeeper, a bigger defeat could have been inflicted upon the Clydesdale Bank Premier League leaders.
On the face of it, there was an element of do-or-die about Smith's line-up.
Algeria international Madjid Bougherra was left out after his late return from World Cup duty, the third time he had transgressed in such a way, meaning 17-year-old Danny Wilson again partnered veteran David Weir in central defence to make his home debut in Europe.
However, Lee McCulloch being pulled back to make it a back three in a 3-4-3 formation hinted at a more positive approach than normally associated with Smith.
That perception was bolstered by the inclusion of striker Kris Boyd, often overlooked for European ties, who, curiously, made his first start in the Champions League.
However, although Stuttgart's 1-1 draw with Hertha Berlin at the weekend left them without a win in six games, there was a nervousness around Ibrox at kick-off, inspired by 4-1 defeats at home to both Unirea Urziceni and Sevilla in the previous two home European games.
And whatever positive vibes the Rangers team sheet was supposed to elicit evaporated in the early stages as the hosts were pressed back by a slick visiting side driven on by an unusually large travelling support.
In the seventh minute McGregor threw himself to his left to push a decent drive from Stuttgart's German international striker, Cacau, past the post.
The opening goal for the visitors, though, was not far off.
Hleb drifted past Whittaker inside the box and cut the ball back to striker Pavel Pogrebnyak who missed his shot but Rudy, perfectly positioned behind him, was not so wasteful.
The home fans were in immediate uproar and moments later there was almost cause for more despair when a free-kick by Kuzmanovic went in off the post but skipper Mathieu Delpierre was ruled offside.
As the Light Blues fought back, with most of the emphasis on the fight, Boyd missed a sitter, heading over from 10 yards after Kenny Miller dropped a cross on to his head.
The first half ended with the Rangers fans still hopeful but the start to the second half was more subdued, both on and off the pitch.
Stuttgart remained on top, probing at the heart of the Ibrox defence as the home side huffed and puffed to garner possession.
There was no surprise though, when, just before the hour mark, Kuzmanovic headed in number two from Rudy's cross.
An air of acceptance rather than anger swept through the Rangers support.
McGregor spared further blushes when he made a fine double save, first from Cacau and then from Pogrebnyak, who followed in the rebound only to drive against the goalkeeper's outstretched legs.
Cult hero Nacho Novo came off the bench to replace Miller but it was an exercise in futility.
The visitors were cruising and almost made it 3-0 in the 78th minute, Pogrebnyak crashing a shot from 14 yards off the outside of the post with the Rangers defence in tatters.
Five minutes from the end McGregor again thwarted Pogrebnyak as the big Russian fired in from close range.
The goalkeeper made further saves from Stuttgart substitutes Thomas Hitzlsperger and Timo Gebhart, and the final whistle could not come quickly enough for the home side.
As the Rangers support dissipated slowly into the Govan night their Stuttgart counterparts taunted them with the Celtic standard 'You'll never walk alone'.
It was the final insult.