At the top, unbeaten leaders Bayern Munich maintained their 100 percent home record when Franck Ribery's second-half strike gave them a 1-0 win over a well-drilled and stubborn Bayer Leverkusen.
VfL Wolfsburg stayed second, seven points behind the Bavarians, by winning 3-1 at Hanover 96 and surprise package Augsburg moved up to third by beating Cologne 2-1, their fourth win on the trot, with a last-minute goal by Alexander Esswein.
Brazilian brothers Raffael and Ronny were on opposite sides as Borussia Moenchengladbach ended a run of three defeats by beating Hertha Berlin 3-2. Raffael scored Gladbach's second goal while Ronny came on as a first-half substitute for Hertha.
Stuttgart never recovered after Choupo-Moting got in front of a dozing defence to flick Tranquillo Barnetta's free kick into the net after 53 seconds.
Stuttgart, who had given new coach Huub Stevens a winning start in Freiburg last week, collapsed dramatically as Max Meyer scored from close range and Choupo-Moting rose unmarked to head Schalke into a 3-0 lead after 21 minutes.
Fifth-placed Schalke, themselves beaten 5-0 at home by Chelsea in the Champions League 10 days ago, added a fourth with another header by the German-born Cameroon forward just after the hour.
Stuttgart's fans watched in silence and not even their mascot, Fritzle the crocodile, could muster any energy as he watched his side lose their fifth home game out of seven this season.
"They scored their first goal far too easily and our whole game plan went down the drain," said Stuttgart goalkeeper Sven Ulreich. "A relegation battle is no fun at all."
Fourth-placed Leverkusen made life tough for Bayern and were gifted an early chance when a mix-up between Xabi Alonso and Jerome Boateng sent Karim Bellarabi clear. His shot beat Manuel Neuer but was cleared off the line by Juan Bernat.
Neuer also needed to make one of his customary forays upfield to clear the danger when Gonzalo Castro got free of the Bayern defence and Stefan Kiessling squandered an exchange counter-attack.
Inevitably, Leverkusen were made to pay for missing their chances when Ribery hooked home following a corner five minutes after halftime.
Bayern forward Robert Lewandowski then missed an open goal from six metres but, with Leverkusen looking incapable of a fightback, it did not matter.
(Writing by Brian Homewood in Berne; editing by Toby Davis/Mitch Phillips)
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