Kevin Volland and Roberto Firmino scored for the visitors.
Read how all the action unfolded below:
2.01pmGood afternoon! With just under half an hour until kickoff in the first of two Bundesliga games this afternoon, let's take a look at the team news for Stuttgart and Hoffenheim.
2.03pmSTUTTGART STARTING XI: Ulreich, Sakai, Schwaab, Boka, Rudiger, Kvist, Leitner, Gentner, Maxim, Ibisevic, Werner
2.05pmHOFFENHEIM STARTING XI: Casteels, Beck, Johnson, Abraham, Vestergaard, Polanski, Firmino, Strobl, Elyounoussi, Volland, Modeste
2.07pmSTUTTGART SUBS: Kirschbaum, Rocker, Khedira, Rausch, Harnik, Cacau, Abdellaoue
2.09pmHOFFENHEIM SUBS: Grahl, Thesker, Sule, Toljan, Rudy, Schipplock, Herdling
2.12pmHoffenheim have made a prolific start to the season in front of goal, scoring 10 goals in their opening three Bundesliga. Anthony Modeste starts as the lone striker for the visitors, but they have a midfield more than capable of adding to the score.
2.15pmStuttgart are still looking for their first points of the new season, having lost their opening three matches, and have been knocked out of the Europa League by Croatian side HNK Rijeka. However, striker Vedad Ibisevic has been in form since the start of the new season, and will surely be keen to add to his goal tally again this afternoon.
2.18pmThis afternoon will see Thomas Schneider take charge of Stuttgart in a Bundesliga match for the first time. The former player, who had been in charge of the club's Under 17s, replaced Bruno Labbadia earlier this week.
2.22pmWhen these two sides met last season, they each took an away win. Stuttgart beat Hoffenheim by a single goal last time two played, but today's visitors won 3-0 in this fixture last year.
2.26pmWith just a few minutes until kickoff, it's time to make a prediction. Stuttgart are a much better side than their three defeats suggest, but Hoffenheim have been really strong in front of goal in the last month, and I can't see that changing. I think I'm going for a 3-1 Hoffenheim win this afternoon.
2.28pmThe players are in the tunnel getting ready to head out for this afternoon's match.
0 minStuttgart get the first half underway.
3 minIt's a bright if slightly frantic start by the home side as they look to pass the ball around the midfield. However, a clumsy challenge by Boka gives the visitors a free kick. Stuttgart quickly win the ball back, allowing Werner to go on the counter attack before crossing the ball in for Leitner, but the midfielder takes too long to line up his shot, allowing Johnson to make the clearance for the visitors.
6 minJohnson gets up front for Hoffenheim, looking to delivery the ball into the box. He loses possession to Schwaab, who attempts a back pass to Ulreich in the Stuttgart goal, but the keeper is left stretching as Schwaab completely mis-hits it. Meanwhile, Hoffenheim are starting to string together their passes well in midfield and are beginning to look the stronger of the two sides.
9 minStuttgart are starting look more composed than they had in the opening couple of minute, and they manage to pin Hoffenheim back inside their own half. Eventually, the visitors manage to find a way through, allowing Polanski to take a shot. It looked like it might have been going wide, but Ulreich didn't take the change, diving to his right to take the catch.
11 minCHANCE! On the counter attack, Leitner wins the ball around 30 yards out and attempts to drill it in from range. It takes a deflection and goes behind for a corner, which Polanski eventually clears.
12 minGOAL! Stuttgart 1-0 Hoffenheim (Rudiger)
13 minHoffenheim are caught napping as Polanski concedes a free kick, which the home side take quickly. Maxim crosses it superbly into the box and it drops to Antonio Rudiger to knock it in from close range for his first goal for the club.
15 minHoffenheim have a chance to get themselves back on level terms with a free kick around 30 yards out. Janick Vestergaard lines up the delivery, electing to go for goal, but his shot is always rising, and ends up in the crowd.
17 minHoffenheim win a corner, but tempers flare ahead of the set piece. The players are still tense as they prepare for the corner, leading to Verstergaard committing a foul inside the box to give Stuttgart a free kick.
18 minCHANCE! A superb ball into the box from Firmino drops to Modeste, who beats Schwaab with impressive pace to leave him with just Ulreich to beat, but the Hoffenheim striker drags his finish inches wide of the post.
19 minGOAL! Stuttgart 2-0 Hoffenheim (Ibisevic)
21 minStuttgart get the better of Hoffenheim at a set piece yet again, as Maxim whips the ball in from a corner, picking out Vedad Ibisevic, who nods the ball in with a textbook header for his seventh goal in all competitions this season. The home side have been clinical when they've had chances during this game, and it's paying off.
23 minCHANCE! Andreas Beck is brought down by Ibisevic around 25 yards out, giving the visitors another free kick from a strong position. Vestergaard takes it again, and this time keeps it on target, but he doesn't get enough power behind the ball, giving Ulreich a comfortable save.
25 minFirmino displays some brilliant footwork out wide before curling the ball in towards the Stuttgart goal, but his cross fails to find his teammates, allowing Ulreich to claim the ball.
27 minGOAL! Stuttgart 2-1 Hoffenheim (Volland)
28 minKevin Volland gets the visitors back into the game with a powerful volley from the edge of the box. It took a deflection off Rudiger on the way in, but Volland had the shot on target anyway.
28 minGOAL! Stuttgart 3-1 Hoffenheim (Maxim)
30 minIt's a shocker for Hoffenheim keeper Koen Casteels. Alexandru Maxim breaks from the re-start, leaving himself with only the visiting keeper to beat. Casteels comes to the edge of the box in an attempt to clear the ball, but he mis-reads the bounce, leaving Maxim an open net to tap in to. What a lively opening 30 minutes it's been!
32 minCHANCE! A long ball towards the box drops to Werner, who tries to drive it in from the edge of the box, but he slices his effort just wide.
34 minDespite the scoreline, Hoffenheim are by no means out of this. They've created some good chances so far, but their midfield haven't been linking up with striker Modeste as much as they could. He'll be key if they're to get back on level terms.
36 minHoffenheim try to build patiently from midfield, before Johnson passes to Strobl, who spots a gap in the Stuttgart defence, and unleashes a rocket from 35 yards. It doens't trouble Ulreich, but it's not far off the target.
38 minPENALTY APPEAL! The visitors win a corner, which is curled in to the head of Modeste. It's blocked by Kvist, but the striker is convinced that the Stuttgart defender gets a hand to it. Looking at the replay, it was actually some brave defending by Kvist, who took the header straight in the face.
40 minBOOKING! Kvist and Modeste get in each others way again moments later on the edge of the box, giving the visitors a free kick. Kvist is shown the first yellow card of the game for persistent offending.
43 minCHANCE! Werner breaks free from Vestergaard before trying to loft it over Casteels, but he fails to keep him effort on target.
45 minThe pace just seems to have gone out of the game as half time approaches. It's not surprising, as the opening half hour was played at quite a tempo. There's just one minute of stoppage time to be played.
45+1 minDISALLOWED GOAL! Tarik Elyounoussi superbly chips the ball over Ulreich from the edge of the box, thinking that he had added a second goal for Hoffenheim, but the referee believes that the keeper has been fouled, and rules it out.
45+2 minHALF TIME: Stuttgart 3-1 Hoffenheim
3.20pmSo Stuttgart head into their break with a two-goal cushion intact, despite Hoffenheim finding the back of the net for the second time just before the whistle.
3.23pmDespite the scoreline, the sides have been quite evenly matched in the opening 45 minutes. Hoffenheim have had the better of the play in midfield, but have lacked accuracy in front of goal, while Stuttgart have been near flawless from set pieces.
3.27pmLet's take a look at some of the stats from the first half. Hoffenheim just edged the possession, claiming 51%. Both sides has seven shot, but crucially, Stuttgart had four on target, compared to the visitors, who had just the one.
46 minHoffenheim get the second half underway.
46 minBOOKING! This is actually one left over from the first half. Abraham picked up a caution for giving the referee his opinion on the disallowed goal at the end of the first 45 minutes.
47 minGOAL! Stuttgart 4-1 Hoffenheim (Ibisevic)
48 minWhat a start to the second half for the home side. Vedad Ibisevic has been in immense form at the start of the season as he's showing no signs of dipping any time soon. Sakai wins the ball in the air, heading it forward for the Bosnian striker, who blasts it in from close range.
50 minCHANCE! Ibisevic gets the ball again on the edge of the box, but he rushes his shot, clearly thinking about his hat-trick, and ends up wasting the chance, thumping the ball well high of the crossbar.
51 minRudiger gives away a free kick near the corner flag, which Volland crosses in for Hoffenheim, but it manages to miss everyone in the box. The visitors manage to pick up the loose ball and win a corner but Polanski loses to ball to Leitner, ending the Hoffenheim threat.
55 minGOAL! Stuttgart 5-1 Hoffenheim (Maxim)
56 minWow, what a finish! Maxim times his run from midfield perfectly before curling it in to the top right corner from the left side of the box, leaving Casteels no chance of making the save.
56 minBOOKING! Maxim is shown a yellow card for removing his shirt while celebrating his goal.
59 minSUBS! It's a double change for the visitors, and a positive one, as Anthony Modeste and Eugen Polanski make way for Sebastian Rudy and Sven schipplock. That should see Hoffenheim switch to a 4-4-2 formation.
60 minCHANCE! The visitors haven't given up yet. Firmino gets on the end of a Elyounoussi cross before attempting a shot from close range, but he just misses.
63 minGOAL! Stuttgart 6-1 Hoffenheim (Ibisevic)
64 minIbisevic seals his hat-trick with a simple header into an empty net. Werner delivered a high ball into the area, which Casteels came out to clear, but missed, gifting the striker an easy finish for a well-deserved hat-trick.
67 minSUB! Ibisevic's teammate Alexandru Maxim won't be completing the team's second hat-trick of the game, as he's replaced by Cacau for the last 20 minutes or so.
69 minCHANCE! Schipplock makes a brilliant run down the wing before attempting to cross in for Volland, but Ulreich is alert to the danger, and comfortably takes the ball for Stuttgart.
71 minCHANCE! Firmino sends the ball in for Volland, who just manages to keep the ball in play before pulling it back for Schipplock. the striker's effort is saved, but it wouldn't have counted anyway, as the referee blows for a foul on Ulreich.
72 minBOOKING! Kevin Volland gets a yellow card for a frustrated challenge on Cacau.
73 minSUB! Moritz Leitner makes way for Martin Harnik for the home side.
75 minSUB! Hoffenheim make their last change of the game, sending on Kai Herdling in place of Tarik Elyounoussi.
77 minCHANCE! Ibisevic appears to look for his fourth goal of the afternoon, but spots Werner running in behind him and selflessly pulls it back for his teammate, but the striker fails to find the target.
79 minThe visitors win a free kick, and Herdling, who has just come on, tries to rally the team, shouting at his teammates to get up front. You have to give Hoffenheim credit for not sitting back despite the five-goal deficit.
80 minSUB! Stuttgart bring on Rani Khedira, with Williams Kvist, who was booked in the first half, coming off.
83 minThe home side seem to have started to shut down, knowing that they've had the win in the bag for quite some time now. Hoffenheim are still trying to chase the ball down, but they're starting to look tired, having been well beaten by their opponents this afternoon.
86 minStuttgart pick up the pace again, with Werner and Boka both waiting in the area, but Johnson manages to run the ball away from danger for the visitors.
88 minGOAL! Stuttgart 6-2 Hoffenheim (Firmino)
89 minRoberto Firmino adds a late consolation for the visitors, chipping the ball over Ulreich in the home goal. The midfielder has been one of Hoffenheim's most productive this afternoon, and the goal in no more than he deserved.
90 minFULL TIME: Stuttgart 6-2 Hoffenheim
4.20pmThe officials don't bother with stoppage time, ensuring that Stuttgart claim their first win of the new Bundesliga season, lifting them up to 14th in the league table.
4.21pmThat's all from the Mercedes-Benz Arena this afternoon, but stick around for more Bundesliga coverage, as Frankfurt play Borussia Dortmund shortly. Thanks for joining me this afternoon, goodbye.