Max Kruse, Christoph Kramer and Filip Daems all scored for Lucien Favre's men as Hannover were given short shrift at the Borussia Park Stadion.
The home side made it clear right from the whistle that they were motivated to win their first home game of the season and Raffael nearly got them off to a flyer in the first minute.
Kruse also went close and the Foals were also unlucky not to be awarded a penalty in the 12th minute, although they did not have to wait too much longer before going in front with Raffael pulling the ball back to Kruse to open his account for his new club.
Not happy to sit on a one-goal lead, Gladbach continued to attack, and they created further chances before Mame Diouf nearly snatched an equaliser against the run of play.
Hannover reorganised during the interval and emerged with a more attack-minded side, but they soon found themselves chasing a two-goal deficit.
Kruse was denied by Ron-Robert Zieler with another effort turned onto a post by Salif Sane, although there was nothing either the Hannover goalkeeper or defender could do about Kramer's follow up.
The final goal came from the penalty spot after Hiroki Sakai handled the ball. Captain Daems stepped up to convert and earn Gladbach their first win of the season.