Raffael gave Gladbach a deserved half-time lead after latching on to a neat pass from Patrick Herrmann, with Sweden international Oscar Wendt settling the result with a sweetly struck volley.
Lucien Favre made no changes to his Gladbach side that had beaten Nuremberg before the international break, while Antonio Rudiger replaced Karim Haggui in the hosts' defence.
Granit Xhaka was enterprising early on for the visitors but failed to test Sven Ulreich with two early long-ranger strikes.
Ulreich kept Raffael out as he advanced on goal in the 17th minute with Max Kruse wasting the rebound by hitting his shot into the side-netting.
But Raffael was not to be denied eight minutes before half-time, picking up Herrmann's reverse pass and holding off Rudiger's challenge before rounding Ulreich and slotting into the net.
Juan Arango and Kruse brought fine stops out of Ulreich after the break, but he had no answer in the 73rd minute as Wendt was afforded space on the edge of the area to power a bouncing ball home.
Victory for Gladbach was their second on the road this season and fourth in a row, leaving them four points clear of fifth-placed Wolfsburg ahead of the weekend, while Stuttgart could drop from eighth to 12th if results go against them.
