Ibisevic scored the only goal of the match in the 30th minute to lift his side, who have now collected seven points in their past three matches, up to 12th place.
Hamburg saw their four-match undefeated streak come to an end and have 10 points to leave them 10th.
Stuttgart had a chance after just two minutes as Ibisevic fed Martin Harnik, who could not beat Hamburg goalkeeper Rene Adler.
The visitors were close again at the quarter-hour mark as Ibisevic shot just right of goal from 12 yards out.
Stuttgart finally grabbed the lead after 30 minutes with Christian Gentner feeding Harnik down the right. The Austrian crossed into the middle where Ibisevic beat Michael Mancienne to the ball and fired home.
Hamburg appeared to have equalised in the 45th minute but Artjoms Rudnevs was ruled offside after Milan Badelj's 30-yard strike blasted off the crossbar.
The hosts had a double chance after 58 minutes with Adler stopping Maximilian Beister's attempt from 17 yards and then Marcell Jansen headed over the crossbar from 11 yards.
The visitors continued their push forward but Raphael Holzhauser's left-footed attempt went just inches wide of the far right post after 65 minutes.
Stuttgart goalkeeper Sven Ulreich needed a quick reaction to save Rafael van der Vaart's blast in the 73rd minute.
Stuttgart failed to convert two more chances in the 79th minute with Ibrahima Traore's shot stopped by a Hamburg defender and Adler blocking away Harnik's follow-up shot.
Ulreich matched Adler with two saves against Jansen and Son Heung-min in the 81st minute.