Stuttgart doubled their lead just seven minutes later when Ibisevic scored his first of the afternoon with a powerful header to give Koeen Casteels little chance in the Hoffenheim goal.
Kevin Volland pulled a goal back for Hoffenheim against the run of play with a curled finish from just inside the area.
However, Maxim added a third with a calm finish from the right side of the box following another flowing passing move from the home side.
Stuttgart ended the match as a contest with three goals inside 15 minutes just after the break, with Ibisevic scoring his second of the afternoon by drilling the ball into the bottom corner in the 47th minute.
Maxim continued an impressive afternoon on a personal level by making the score 5-1 when he fired the ball past a helpless Casteels.
Ibisevic completed the scoring for the hosts with another towering header as Stuttgart continued to dominate the contest.
Roberto Firmino took advantage of some poor defending to slot home a consolation goal for Hoffenheim late on but an emphatic victory for Stuttgart had already been secured.