The away defeat capped a week to forget for Julian Nagelsmann's Leipzig after its 5-0 thumping at Manchester United in the UEFA Champions League.
Leipzig forwards Yussuf Poulsen and Dani Olmo both wasted chances while Gladbach had a goal by Alassane Plea ruled offside.
Austrian winger Hannes Wolf, 21, who is on loan from Leipzig this season, sealed the win with his first Bundesliga goal on 60 minutes before Plea hit the post.
"I've waited a year and a half for this moment. It's taken a lot off my mind," Hannes, who joined RB Leipzig in 2019 but failed to break into the first-team, said.
"I see myself as a Borussia Moenchengladbach player and hope to be here for longer just than this year."
The result leaves Leipzig third and Gladbach fourth, with Bayern Munich staying top after its win against FC Cologne.