Dutch striker Klaas-Jan Huntelaar completed a quick break for the visitors two minutes after the restart to give Schalke the lead and raise hopes of banishing Monday's first round defeat by third-tier Dynamo Dresden.
Hanover, who had Germany keeper Ron-Robert Zieler to thank for keeping them in the game, levelled through Edgar Prib in the 67th after he connected with a Leonardo Bittencourt cross in their first real chance of the game.
New arrival Joselu's thundering drive in the 70th completed an unexpected comeback for Hanover, with Schalke having only themselves to blame for failing to hold on to their lead.
Hoffenheim also got off to a winning league start after scoring twice in two minutes through new signing Adam Szalai and Tarik Elyounoussi to beat Augsburg 2-0.
Hertha Berlin also took a two-goal lead with a brace from Julian Schieber but squandered it in the second half to settle for a 2-2 draw with visitors Werder Bremen.
Eintracht Frankfurt gave new coach Thomas Schaaf a winning debut after edging Freiburg 1-0 courtesy of a first half Haris Seferovic strike.
Champions Bayern Munich made a winning start to their league season, edging past VfL Wolfsburg 2-1 on Friday while runners-up Borussia Dortmund take on Bayer Leverkusen later on Saturday.
- Sports & Recreation