Madjid Bougherra's second-half equaliser salvaged a draw for Rangers in a game which for long periods looked beyond them. The Algeria international fired home a low shot into the bottom corner much to the delight of the large contingent of fans who had made the trip from Glasgow.
Rangers had been dealt a blow ahead of the game with the news that captain David Weir was ruled out through injury. Stuttgart, however, received a boost when Alexander Hleb made the starting line-up after being rated doubtful with a muscle strain.
Rangers found themselves under pressure with less than a minute on the clock when Cacau ran on to a cross from the right and drew a decent save from goalkeeper Allan McGregor, before Thomas Hitzlsperger hooked the rebound over the crossbar.
The home side threatened again when Cacau released Pavel Pogrebnyak into the box and he teed up Hleb who was denied from close range by McGregor at the near post.
However, the Rangers goalkeeper was picking the ball out of the back of the net after 18 minutes when Cacau's cut-back found Pogrebnyak who dispatched a powerful right-foot shot past McGregor. Rangers looked nervous when in possession but Steven Davis released Kenny Miller through on goal but keeper Jens Lehmann was first to the ball to snuff out the chance.
Rangers appeared more composed when they emerged for the second half and could have restored parity within a couple of minutes of the restart.
Jerome Rothen picked out Sasa Papac in front of goal and the left-back did well to hold off Matthieu Delpierre only to see his header flash across the face of goal and wide of the upright.
At the other end, a Pogrebnyak ball found Roberto Hilbert out on the right but his shot rippled the side-netting.
It was Lehmann's turn to be called into action when Miller tried his luck with a long-range effort that the Stuttgart goalkeeper managed to block at the near post. But he could not stem the tide for long. Bougherra worked a one-two with Rothen before driving past Lehmann.
Rangers could even have snatched a last-gasp victory, hitting the woodwork in the final minute of the game when a Davis shot struck the post.
Stuttgart (4-4-2): Lehmann; Trasch, Tasci, Delpierre, Boka; Hilbert, Hitzlsperger, Khedira, Hleb (Gebhart, 67); Cacau (Schieber, 88), Pogrebnyak. Substitutes not used: Ulreich (gk), Boulahrouz, Marica, Celozzi, Kuzmanovicr.
Rangers (4-5-1): McGregor; Whittaker, McCulloch, Bougherra, Papac; Naismith, Davis, Thomson, Mendes; Rothen; Miller (Novo, 90). Substitutes not used: Alexander (gk), Boyd, Beasley, Smith, Fleck, Little.
Referee: M Busacca (Switzerland).