Didier Ya Konan and Mame Diouf scored the goals for Mirko Slomka’s men, with Havard Nordtveit setting up a grandstand finish between the two sides who end the weekend just one position, but 10 points apart in the table.
Gladbach have now not won in three games and risk falling further behind in the chase for a place in the group stages of the Champions League next season.
Hannover, meanwhile, are now just four weeks short of going a full year unbeaten at home in the Bundesliga and they will head into Thursday’s Europa League quarter-final second-leg tie with Atletico Madrid in confident mood.
Both sides showed plenty of confidence in the early exchanges of a high-tempo game.
Marco Reus was pulling all of the strings for Gladbach while Ya Konan and Diouf showed signs of their excellent recent form with the only thing lacking in the first half being a goal.
Ya Konan remedied that in the 57th minute when he Konstantin Rausch’s shot turned into an assist for the Ivory Coast striker, who slid in to thread the ball through the legs of Marc-Andre ter Stegen at full stretch.
Jan Schlaudraff set up the second goal with a cross whipped in from the right which Diouf only needed to flick with his head into the far corner.
Gladbach responded just a few minutes later with Nordtveit allowed to advance with the ball at his feet and evade one desperate lunge before shooting low into the bottom left-hand corner of the goal from the edge of the penalty area.
The visitors laid siege to the Hannover goal in search of an equaliser and they almost got one in the last minute when Reus’s shot was tipped over by Ron-Robert Zieler.
There was confusion and a penalty appeal from the resulting corner, but the referee blew his whistle as soon as the Reds finally cleared their lines, and it was the final whistle.