Cacau, fresh from his four-goal haul against Cologne at the weekend, gave Stuttgart a deserved half-time lead but Ibrahimovic struck just after the interval to put Barca in the box seat heading into the second leg at the Nou Camp.
Barca were boosted by the return to action of Xavi and Ibrahimovic, who both missed Saturday's 4-0 win over Racing Santander through injury, but neither of them had much chance to shine in the first half.
The home side, who have improved immensely under Christian Gross and had won six of their previous seven games, were determined to take the game to Barca and were rewarded when Cacau broke the deadlock in the 25th minute with a powerful header.
Timo Gebhart's cross from near the touchline was inch-perfect, just clearing Carles Puyol at the far post and allowing Cacau head past the helpless Victor Valdes.
Cacau had a chance to make it 2-0 in the 32nd minute after picking up Pavel Pogrebniak's knock down near the halfway line and sprinting towards the Barca box, but this time Valdes was equal to the Brazil-born German international's effort.
Stuttgart were refusing to let the reigning champions settle and created another opportunity in the 35th minute following good work by on-loan Barca player Alexander Hleb.
Christian Trasch wasted the chance though, slicing his shot well wide from the edge of the area.
Barca's much-vaunted attack were getting little change out of the Stuttgart defence, but from nowhere they almost grabbed an equaliser five minutes before the break.
Lionel Messi, who had been his side's main threat, fired in a shot from 25 yards that looked set to creep in at the far post after only being half stopped by Stuttgart goalkeeper Jens Lehmann.
However, the ball struck the post and rebounded back into the veteran's arms.
A minute later Stuttgart created another opening when Pogrebniak burst past Gerard Pique and Valdes was again called upon to save his side.
Barca fans might have been fearing the worst at the break, but they need not have worried as the Catalan giants looked much more comfortable in the second half.
It took Pep Guardiola's side just seven minutes to get back on level terms thanks to Ibrahimovic.
Pique used his 6ft 3in frame to good effect to nod a high ball down to Ibrahimovic, and although Lehmann blocked his first effort, the Swede slotted home at the second attempt.
Ibrahimovic looked certain to put Barca ahead in the 67th minute after Lehmann had failed to collect a corner, but the former Inter Milan striker's goal-bound shot struck Cristian Molinaro on the line and rebounded over the bar.
Barca were enjoying much more quality possession but Stuttgart were still pushing forward whenever they could and Valdes did well to smother Ciprian Marica's shot at point-blank range.
Barca were also keen to force a winner, but neither side could find a winner in the closing stages.
IBRAHIMOVIC SPARES BARCA BLUSHES
