After Lucien Favre resigned as a response to six successive defeats in all competitions, interim boss Andre Schubert led the team to a 4-2 win against Augsburg in midweek and he boosted his chances of landing the job on a permanent basis as his side climbed away from the bottom three.
After failing to carry much of a threat for long spells of the first half, Stuttgart were gifted the chance to reduce the deficit before the break when Daniel Didavi was brought down by Havard Nordtveit in the box.
Daniel Ginczek stepped up from 12 yards and he fired home the penalty to keep the pressure on the visitors heading into the interval.
However, it was Gladbach who were the brighter of the two sides early in the second half and only some fine goalkeeping from Przemyslaw Tyton prevented Raffael from finishing after getting clear of the last defender.
Stuttgart did enjoy spells on top as they went in search of an equaliser, but the hosts wasted their best chance when Timo Werner headed just over the crossbar, before Yann Sommer made a vital save to push Alexandru Maxim's effort past the post.
Gladbach punished them for failing to take one of the opportunities as Schubert's side wrapped up the win in stoppage time when Raffael led the counter to sprint clear before calmly slotting past Tyton to secure the points.