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 half time.
"We have to do better, play the way we are capable of, but don't forget that in European competition you are facing very good teams," said Barca coach Pep Guardiola.
"Europe is very tough, very difficult and very demanding."
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.
In another home attack Christian Traesch should have done better when he shot wide from Aleksandr Hleb's layoff.
"I think we could have had another goal but things changed in the second half," said Gross. "They (Barca) didn't create so many chances.
"It was a great first half but we couldn't keep it up for the second. Not many teams take points off Barcelona so this makes me happy."
