Brazilian-born German international Cacau headed the mid-table Bundesliga team in front in the 25th minute as they outplayed the visitors in a pulsating first half.
Stuttgart had chances to increase their lead as they put the champions on the back foot but Lionel Messi also hit the post for Barca just before halftime.
Barca levelled in the 52nd minute when Ibrahimovic scored at the second attempt after his first shot was superbly saved by Jens Lehmann.
The first chance of the game fell to Messi, who had a shot blocked by Serdar Tasci after he burst through the middle.
Cacau, who scored four goals in a 5-1 win at Cologne on Saturday, then put Stuttgart ahead when he outjumped Carles Puyol at the far post to nod in Timo Gebhart's cross.
The Germans appealed for a penalty for a handling offence by Gerard Pique before Cacau had a toe-poked shot blocked by keeper Victor Valdes.
In another home attack Christian Traesch should have done better when he shot wide from Aleksandr Hleb's layoff.
Stuttgart then had a let-off when Lehmann allowed a Messi shot to slip through his hands, only for the ball to hit the post and bounce into the arms of the grateful keeper.
Barca were on target soon after the restart when a Pique header found Ibrahimovic and he converted from close range at the second attempt.
The Sweden striker almost grabbed a winner when his shot was deflected over by a defender after Lehmann completely missed a corner.
Stuttgart coach Christian Gross was frustrated his side were only 1-0 up at halftime.
Bordeaux on course
Girondins Bordeaux are on course to reach the Champions League quarterfinals for the first time after Michael Ciani's first half header earned Laurent Blanc's side a 1-0 victory at Olympiakos Piraeus on Tuesday.
Bordeaux, who amassed more points than any other team in the group stage, soaked up late pressure and were good value for a last 16 first-leg win that makes them favourites to progress ahead of the return at the Stade Chaban-Delmas on March 17.
Olympiakos had booked their place in the last 16 by finishing second in Group H thanks largely to their home form and, roared on by a typically passionate crowd, began strongly.
Olof Mellberg threatened first, heading Jesus Datolo's free-kick just wide after four minutes.
Wingers Datolo and Lomana Lua Lua also saw plenty of the ball early on and had Bordeaux on the back foot with their pace and trickery.
The home side's best chance of the game came with just under 10 minutes lift when former English Premier League forwards Matt Derbyshire, on as a second half substitute, and Lua Lua combined bur the latter saw his shot tipped around the post.
The hosts, who were playing in their 200th European game, had a goal chalked off in the closing seconds as they pushed for an equaliser, Derbyshire adjudged to having fouled goalkeeper Cedric Carrasso as Enzo Maresca nodded home from close range.
Benfica through
In the Europa League two goals by Paraguay striker Oscar Cardozo helped Benfica to a 4-0 win over Hertha Berlin to clinch a place in the last 16. Benfica opened the scoring when Argentine Javier Saviola set up compatriot Pablo Aimar in the 25th minute and the playmaker beat Jaroslav Drobny with a fine diagonal shot.
The Bundesliga's bottom club fell further behind when Cardozo headed in just after halftime. Spaniard Javi Garcia netted in the 59th minute and Cardozo volleyed in three minutes later to complete a 5-1 aggregate victory.
Reuters