Wolfsburg's hopes of breaking into the German Bundesliga's top four suffered a setback on Sunday after being drubbed 6-2 at mid-table Hoffenheim.
Wolfsburg finished the match with ten men as German international Christian Traesch was sent off.
Dieter Hecking's Wolves had hoped for three points in Hoffenheim to take fourth spot from Schalke, who were routed at runaway league leaders Bayern Munich on Saturday.
Croatia forward Ivan Perisic pulled a goal back for Wolves with 15 minutes left.
But the visitors had right-back Traesch sent off for a foul in the area and Hoffenheim's Sejad Salihovic netted the penalty before Modeste's replacement Sven Schipplock hit their sixth.
Wolfsburg's result leaves them fifth.
It means all three teams immediately behind leaders Bayern Munich and second-placed Borussia Dortmund, who beat Nuremberg 3-0 on Saturday, suffered defeats over the weekend.
Stuttgart are fourth from bottom after losing 2-1 at Eintracht Frankfurt in what was a club record eighth straight defeat and heaped further pressure on coach Thomas Schneider.