Schalke started its Bundesliga season with a 3-0 victory at Werder Bremen on Saturday while promoted Ingolstadt claimed its first top-level win.
Bremen defender Theodor Gebre Selassie scored an own goal with an unstoppable chip in off the underside of the bar while trying to clear Joel Matip's cross in the 34th.
Matip then set up Eric Maxim Choupo-Moting in the 68th and Klaas Jan Huntelaar rounded off the scoring in the 85th after a brilliant run from Leroy Sane.
Ingolstadt defeated Mainz 1-0 away thanks to Lukas Hinterseer's 66th-minute winner, Hertha Berlin won 1-0 at Augsburg as both sides finished with 10 men, Bayer Leverkusen came from behind to beat Hoffenheim 2-1 and promoted Darmstadt drew 2-2 at home with Hannover.
Borussia Dortmund was hosting Borussia Moenchengladbach later.