A superb first half display saw them race into a 4-0 lead, with two goals from Nicólas González accompanied by a Gonzalo Castro strike and Tim Kister own goal.
Enrique Peña Zauner pulled one back in a more subdued second 45 minutes, before Hamadi Al Ghaddioui made it five at the death.
Sandhausen blown away in first half
Sandhausen had been in superb form and Uwe Koschinat named an unchanged team here from the one that drew with champions-elect Arminia Bielefeld on Friday. However, after a couple of extremely flat displays against VfL Osnabrück and Karlsruher SC, Stuttgart clearly meant business. There were just two recognised defenders in the line-up, and their attacking intent was clear from the off, with several chances before they took the lead after a delayed kick-off due to the weather.
Philipp Klement’s corner found González, who out-jumped Kevin Behrens to head home. However the goal was controversial with replays clearly showing it should be been a throw-in rather than a corner. The officials missed it but Koschinat didn’t – he was booked for his complaints. It got better for the hosts 20 minutes in. A González ball was seemingly headed away from danger, but Castro, outside the box, volleyed it low and direct.
Sandhausen simply weren’t at the races here. It got worse for them when Silas Wamangituka shrugged off the interest of Leart Paqarada, passed Martin Fraisl then forced an own goal out of Kister. Not long after, Aleksandr Zhirov brought down former Sandhausen man Philipp Förster in the box, with González comfortably dispatching from the spot.
Julius Biada had had a shot saved by Gregor Kobel when the game was 1-0 but Sandhausen’s only other sights at goal in the half came after the fourth. However Paraqada’s free-kick was harmless, and Behrens chose to shoot when it may have been better to pass to Robin Schau. It was an easy take for Kobel instead.
Quieter second half
Stuttgart initially carried on where they left off, with Saša Kalajdžić, making his first start after missing most of the season with injury, seeing a header saved. González came close to a hat-trick as well, but headed a free-kick wide of the far post. After that though, with no real incentive to keep pummelling the Sandhausen defence, they began to ease off.
Sandhausen reminded their hosts they were still there when Behrens had a shot blocked and Biada went wide, and they managed to pull one back from a messy situation after a cross in from Dennis Diekmeier. Peña Zauner, not long off the bench, was the one to capitalise, scoring his first goal for the club, but only a consolation.
The result was a formality but substitute Al Ghaddioui threatened a couple of times to bolster the goal difference – not that they can realistically catch Bielefeld at the top. Two efforts were saved by Fraisl, but with the final kick of the game, he beat the Sandhausen goalkeeper to complete a rout.
So Stuttgart move back into second to put themselves back in control of their own fate. Despite the defeat, results elsewhere ensure that Sandhausen are now 100% safe for another season.
Stuttgart: Kobel, Phillips, Karazor, Kempf; Mangala, Castro, Klement (Egloff 70‘); Wamangituka (Coulibaly 80‘), Förster, González (Stenzel 60‘); Kalajdžić (Al Ghaddioui 70‘).
Sandhausen: Fraisl; Diekmeier, Zhirov, Kister, Nauber (Peña Zauner 64‘), Paqarada; Taffertshofer (Frey HT), Linsmayer; Biada (Türpitz 75‘); Behrens (Bouhaddouz 75‘), Scheu (Engels 64‘).
Goals: González (12‘, 31’), Castro (20‘), Kister (28‘ OG), Al Ghaddioui (90+4’); Peña Zauner (68’).
Referee: Patrick Alt.
Elsewhere on Wednesday
SSV Jahn Regensburg are now safe after a 2-1 win over Karlsruher SC, who remain in the bottom three. Erik Wekesser gave Regensburg the lead, with a quick equaliser from Jérôme Gondorf disallowed by VAR. Sebastian Stolze got a second after the break, with Babacar Gueye getting one back.
VfL Bochum remain the team to beat at the moment though, winning 2-1 at FC Erzgebirge Aue. Thomas Eisfeld and Anthony Losilla scored for them, with Njegos Kupusovic added a consolation after both sides had been reduced to ten men.