After three successive losses, Stuttgart coach Bruno Labbadia was sacked, with former player Thomas Schneider taking on the job.
And the new man would have been delighted with what he saw, as they cruised to victory thanks to a Vedad Ibisevic hat-trick.
Antonio Rudiger opened the scoring in the 11th minute for the winners, tapping Alexandru Maxim's low cross into an empty net, before Ibisevic opened his account against his former team.
Kevin Volland produced a quick response for Hoffenheim but Romanian Maxim pounced on a mistake by Hoffenheim goalkeeper Koen Casteels to restore Stuttgart's two-goal lead.
And Bosnia international Ibisevic's second – scored just after the break when another Hoffenheim error was capitalised on – effectively sealed the result.
Maxim's excellent afternoon continued when he scored Stuttgart's fifth with a delightful curling effort before Ibisevic netted his third goal of the match from a header.
And although Roberto Firmino scored a late goal for the visitors, it was of little consolation as Stuttgart climbed out of the relegation zone in emphatic style.
The day's other fixture saw Dortmund post a 2-1 win at Eintracht Frankfurt as they made it four wins from as many matches this season.
Dortmund – who have lost just twice on the road since September 2011 – took an early lead through Armenian Henrikh Mkhitaryan, when he slotted past Kevin Trapp after a delightful Jakub Blaszczykowski through-ball.
Vaclav Kadlec was a permanent threat for Frankfurt, and went close to scoring twice in the early stages.
Kadlec eventually got his goal shortly before half-time when he pounced quickly to net the rebound after Stefan Aigner's header hit the post.
But Dortmund were well worth their win, as Mkhitaryan got his second with an outstanding left-foot finish after cutting in from the right.
Neven Subotic hit the post with a header as Dortmund pressed for a third goal, but in the end two was enough as Jurgen Klopp's men moved to the top of the league.
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