They continued to press and managed to break the deadlock less than 20 minutes into the match when Sejad Salihovic blasted the ball in from a free kick 20 yards out.
However, Hoffenheim were able to extend their lead shortly before the end of the first half as Jannik Vestergaard headed in from a corner.
Salihovic almost scored his second of the match just after the restart as he drilled the ball towards goal with a shot from outside the box, but it was tipped over.
Altintop continued to look like Augsburg's best chance to get a goal back, but the home side continued to see plenty of the ball as full time approached, allowing them to see out the win.
The result leaves Hoffenheim ninth in the table, while Augsburg sit eighth.