Monchengladbach made the perfect start to the match as they opened the scoring in just the eighth minute through Patrick Herrmann, who collected a clever through-ball from Branimir Hrgota before firing into the bottom corner.
Paderborn's task was twice as difficult six minutes later when Raffael tapped in from close range after seeing his header blocked by Lukas Kruse.
Monchengladbach continued to threaten throughout the first half, but wasted a chance to make it 3-0 before the break when Herrmann struck his effort wide from just a few yards out following a fast counter-attack.
The hosts produced a big response after the break, and were inches away from reducing the deficit when Mario Vrancic saw his free kick pushed away by Yann Sommer.
Hrgota was close to wrapping up the win when he found himself in space on the edge of the box, but his powerful strike rebounded to safety after striking the post.
It appeared that Monchengladbach's wastefulness may come back to haunt them when Jens Wemmer volleyed home in the 70th minute to pull a goal back after linking well with Moritz Stoppelkamp.
However, the visitors survived the inevitable spell of late pressure from Paderborn to hold on for the win.