The home team, meanwhile, will move into the top half of the table if they can avoid defeat.
Stuttgart's lingering hopes of qualifying for next season's Europa League were probably extinguished by their 2-1 defeat away to Union Berlin on Saturday.
The hosts were the more threatening side throughout the affair, particularly during the first half, when Urs Fischer's side managed to secure a two-goal cushion via two superb crosses from the marauding Christopher Trimmel, who found Grischa Promel and Petar Musa to both oblige with fairly routine finishes.
Having made changes at half time, Stuttgart looked capable of mounting a comeback after Sasa Kalajdzic's clever layoff helped Philipp Forster pull one back, but the Union Berlin defence, which Pellegrino Matarazzo had praised prior to the match, stood strong to hold out for victory.
However, while missing out on Europe may be a minor disappointment, a top-half finish would be a perfectly good achievement for Matarazzo and his players given that this is their first season back in the Bundesliga having only been promoted last season.
Wolfsburg, meanwhile, suffered back-to-back defeats for the first time this season after a narrow 3-2 loss at home to reigning champions Bayern Munich.
Jamal Musiala showed England's loss is Germany's gain by displaying dazzling feet before squeezing his strike past Koen Casteels at the near post, before Wolfsburg's goalkeeper made a real howler by dropping a routine cross right into the path Eric Choupo-Moting, who tapped into an empty net for his third goal in four matches.
A loose pass from Thomas Muller in midfield allowed Xaver Schlager to intercept and break in trademark fashion, with the midfielder finding Wout Weghorst, who stroked the ball into the far corner with a fine finish to provide some hope for his side.
Musiala restored Bayern's two-goal cushion with a superb header, but to their credit Wolfsburg made a real fist of a comeback, with Maximilian Philipp pulling a goal back from close range before substitute Jerome Roussillon wasted the Wolves' best chance of equalising, dragging his shot wide from a tight angle.
With their lead over fifth-placed Dortmund reduced to five points with five games remaining, Oliver Glasner's side may not be able to afford too many more slip-ups if they are to avoid a mostly magnificent campaign turning sour at the final stretch.
Stuttgart will remain without Silas Wamangituka for the foreseeable future after the winger sustained an ACL injury last month.
Nicolas Gonzalez is unlikely to return until the end of the month due to a thigh injury, with Wednesday's match against Wolfsburg also likely to come too soon for Lilian Egloff, Clinton Mola, Hamadi Al Ghaddioui and Orel Mangala to feature.
Former Arsenal defender Konstantinos Mavropanos is suspended having picked up his fifth booking of the season against Union Berlin, so Atakan Karazor is primed to drop into the back three, with captain Gonzalo Castro returning to the first XI.
Roussillon is a natural replacement for Otavio at left-back, but with no natural alternative to Mbabu, Ridle Baku may be utilised as an attacking right-back, with Josip Brekalo coming into the side higher up the pitch.
Stuttgart possible starting lineup:
Kobel; Karazor, Anton, Kempf; Stenzel, Castro, Endo, Coulibaly; Forster, Didavi; Kalajdzic
Wolfsburg possible starting lineup:
Casteels; Baku, Lacroix, Brooks, Roussillon; Schlager, Arnold; Brekalo, Gerhardt, Philipp; Weghorst
We say: Stuttgart 1-2 Wolfsburg
While Wolfsburg may miss their first choice full-backs, we still expect them to have a little too much for a stuttering Stuttgart side.
Matarazzo's outfit have desperately missed the pace and power of Wamangituka, with an overeliance on target man Kalajdzic proving easier to defend against.
The Wolves will be highly motivated to bounce back from two successive defeats and ensure they get over the line in terms of qualifying for next season's Champions League.