The Bosnian punished his former club three times with livewire Alexandru Maxim and Antonio Rudiger also on target in Thomas Schneider's first game in charge of the Swabians in the Bundesliga after replacing Bruno Labbadia during the week.
Kevin Volland and Roberto Firmino scored consolations for Hoffenheim, but Markus Gisdol's side had no chance in a local derby.
Rudiger's first professional strike got the goalscoring under way in the 12th minute as he tucked Maxim's cross in from close range.
Maxim was the provider again for Ibisevic's first goal minutes later, the Bosnian rising high to head in from six yards out.
Volland reduced the arrears with a shot which took a wicked deflection off Rudiger to leave Sven Ulreich no chance.
There was no chance of Hoffenheim getting back into the game, though, as Maxim made it 3-1 before half an hour had even been played, accepting a gift after Koen Casteels misjudged a long ball forwards and left his goal gaping.
Ibisevic put the result beyond doubt early in the second half when he rounded Casteels to net his second of the game and Maxim also completed his brace with a neat curling effort into the far corner from just inside the penalty area to the left.
Stuttgart showed no mercy on their local rivals and Ibisevic made it six, completing his hat-trick with a close-range header from Timo Werner's cross in the 63rd minute.
There was still time for Firmino to bundle the ball in for a second consolation for the guests.
Rani Khedira, the brother of Real Madrid and Germany's Sami, came on for his Bundesliga debut, participating in the celebrations at the Mercedes-Benz Arena as Stuttgart finally picked up their first win of the season.