كتب : Hatem Maher
The hosts took the lead after 25 minutes when Brazilian-born German international Cacau out-jumped Carles Puyol at the far post to head home a cross from the right.
Holders Barcelona leveled the score early in the second half through Ibrahimovic, who was recently criticized for his lack of goals.
Defender Gerard Pique headed a Sergio Busquets pass into the path of the Swedish striker, who saw his initial effort blocked by the keeper.
He notched home on the rebound to earn the Catalans a draw against a stubborn Stuttgart side.
Barcelona will be overwhelming favorites to advance to the quarter final when they host Stuttgart on March 17.
Elsewhere, French side Bordeaux put one foot in the last eight after claiming a 1-0 away victory over Greek club Olympiakos.
A header from defender Michael Ciani in the first-half's additional time gave Bordeaux a precious win.
Watch Stuttgart-Barcelona goals