The first chance of the game came the way of the visitors after Pierre-Michel Lasogga, whose header from close range in the seventh minute flew wide.
However, the home side broke the deadlock in the 25th minute when Andre Hahn's cross fell to Kruse, whose initial shot struck the post, but the 26-year-old proceeded to score with his follow-up.
Monchengladbach could have doubled their lead minutes later through Hahn, but his header whizzed past the right post.
Kruse and Raffael had further chances to put the game to bed for the home side in the 50th minute, but both failed to trouble the Hamburg goalkeeper.
Despite the odd foray forward, Josef Zinnbauer's outfit were unable to pull a goal back, and so the game ended with Monchengladbach taking all three points.
The home side climb to sixth place, while Hamburg fall to the foot of the table.