Bruno Labbadia's men had dropped into the bottom three after Augsburg had shared a goalless draw with Nurnberg in the earlier game.
Ibisevic ensured his side were there for only a couple of hours, though, as he struck on the half-hour to grab just Stuttgart's second win in eight league games to start the season.
Bayern Munich made it a record-breaking start to the Bundesliga season by recording their eighth successive win by routing Fortuna Dusseldorf 5-0.
Looking to beat their own record of seven straight wins from the season's outset, they emphasised their current superiority in German football with Mario Mandzukic and Luiz Gustavo giving them a two-goal advantage at half-time.
Thomas Muller added two more for the record German champions and Rafinha rounded off the comprehensive victory in the 87th minute of a one-sided game.
Defending champions Borussia Dortmund slipped further behind rampant Bayern after they were stunned 2-1 by Schalke in the Revier derby.
Ibrahim Afellay and Marco Hoger scored the goals for Huub Stevens' side, who emerged triumphant in the 141st derby encounter between the two sides, with Poland striker Robert Lewandowski's effort proving scant consolation.
Fourth-placed Dortmund are now 12 points adrift of Bayern as well as five behind Schalke in third place and their grip on their title already appears to be slipping after just eight games.
Eintracht Frankfurt bounced back from their first defeat of the season to see off Hannover 3-1 and remain five points adrift of Bayern in second.
The hosts were defeated by Borussia Monchengladbach before the international break but looked firmly on course to return to winning ways after Karim Matmour and Sebastian Jung put them 2-0 ahead.
Although Mohammed Abdellaoue pulled a goal back for Hannover shortly before the break, Alexander Meier made the points safe for Eintracht with eight minutes to go.
Gonzalo Castro's 87th-minute strike rescued a 2-2 draw for Bayer Leverkusen at home to Mainz.
Stefan Kiessling put Leverkusen ahead just before half-time but Adam Szalai and Marcel Risse turned the game on its head before Castro struck late on to ensure the points were shared.
Daniel Caligiuri's strike five minutes before the interval and Julian Schuster's goal in the 84th-minute goal gave Freiburg their first win on the road at rock-bottom Wolfsburg, who suffered their fourth successive defeat.
In the late kick-off, Werder Bremen hammered Borussia Monchengladbach 4-0.
Nils Petersen broke the deadlock in the 37th minute before Marko Arnautovic doubled Bremen's lead on stroke of half-time, with Niclas Fullkrug scoring a minute after being introduced in the 75th minute and Zlatko Junuzovic completing the romp four minutes from time.
Sunday's Bundesliga Results
Saturday's Bundesliga Results
Friday's Bundesliga Result