Martin Harnik put Stuttgart in the lead half-an-hour into the match and the five-time champions should have gone two goals up in the last quarter of an hour but Alexandru Maxim missed a golden opportunity, reports Xinhua.
Minutes before the miss, Eintracht were awarded a penalty which was withdrawn by the referee after consulting the linesman.
Stuttgart paid a heavy price for missing the chance when Eintracht equalised through Jan Rosenthal and nine minutes later Alexander Meier struck the winner.
The victory pushed Eintracht up to 12th position with 25 points while Stuttgart are in 15th with 19 points, ahead of Hamburg SV and Freiburg on goal difference.
In the other match of the evening, Hoffenheim swamped VfL Wolfsburg 6-2 with three of their goals coming in a six-minute spell before halftime.
Hoffenheim were involved in 100 goals in 23 games, scoring 52 goals and ironically conceding 48.
Roberto Firmino put Hoffenheim ahead only to see Bas Dost level the score before Niklas Suele headed Hoffenheim in the lead again and then Frenchman Modeste struck twice to make it 4-1 at the break.
Wolfsburg pulled one back when Ivan Perisic scored, but Sejad Salihovic added a fifth goal converting a penalty and he then paved the way for the sixth for Sven Schipplock.