The hosts started the game brightly, with Tamas Hajnal testing visiting goalkeeper Fabian Giefer after just six minutes.
Fortuna came close in the 22nd minute when Robbie Kruse made an attempt to score, but his effort went just wide.
The two sides created a few other chances during the remainder of the first half, but neither could manufacture anything productive.
Stuttgart crafted a brilliant chance around the hour mark, when Andrey Voronin failed to keep his shot on target from just four yards out.
Christian Gentner then headed just wide of the Stuttgart goal just moments later.
The hosts had the better of the chances thereafter, but eventually had to settle for a point.