Raffael put the hosts in front with the first chance of the game as he volleyed past Stuttgart keeper Ron-Robert Zieler to breathe life into a dull encounter.
The Brazilian forward doubled his tally for the night with just under 20 minutes to go from the penalty spot after Dennis Aogo brought down Thorgan Hazard to ensure Die Fohlen secured three points at Borussia-Park.
Borussia Mönchengladbach boss Dieter Hecking made two changes to the side that drew 2-2 with RB Lepzig on Saturday as Patrick Herrmann replaced Jonas Hofman on the right side of midfield while injured goalkeeper Yann Sommer was replaced by Tobias Sippel.
Hannes Wolf was forced into making one of the two changes to the side that beat VfL Wolfsburg 1-0 as captain Christian Gentner was replaced by Orel Mangala due to the former's horror injury, while Takuma Asano came in for their top scorer Chadrac Akolo.
First-half sees just one shot on target
The first-half was not an exciting spectacle for fans by any means, with just one shot in total managed by both sides over the opening 45 minutes.
Die Fohlen captani Lars Stindl was the man who tested the gloves of Zieler with a low drive from the edge of the box, but that was the closest either side came to breaking the deadlock in a half that lacked attacking quality.
Stuttgart came closest through Mangala on the stroke of half-time as the Belgian lined up to shoot from 25 yards before seeing his strike fly wide of Sippel's goal.
Mönchengladbach midfielder Christoph Kramer was forced off at half-time due to a head injury he sustained in the first 45 and he was replaced by 18-year-old debutant Mickaël Cuisance, who was signed from French side AS Nancy U19 in the summer.
Swabians forward Simon Terodde broke forward in search of his first Bundesliga goal for the club just after half-time but could only drag his shot wide of Sippel's goal from just inside the box.
Hosts controlled the second-half after taking the lead
The hosts became much more incisive in midfield following the introduction of Cuisance, and almost found a way through as Hazard played a one-two with Stindl before being challenged in the box by Marcin Kamiński.
Mönchengladbach finally broke the deadlock with the game's first real chance in the 57th minute as Raffael got on the end of Nico Elvedi's cross to volley past Zieler for his first goal of the season.
Substitute Josip Brekalo tested Sippel from the edge of the area with 20 minutes to go after some good build-up play between him and Aogo out on the left, but his shot was saved by the Mönchengladbach keeper with Terodde just failing to get a touch on it that would have sent it past the German.
Stuttgart full-back Aogo gifted Mönchengladbach a penalty 73 minutes in as he unnecessarily brought down Hazard from a free-kick and afforded Raffael the chance to double his side's lead, and the Brazilian duly obliged from 12 yards sending Zieler the wrong way.
Terodde had a chance to halve the deficit with 10 minutes to go but was slow off the mark and was forced into shooting off balance which saw his weak strike easily saved by Sippel from close range.