Hanover's Konstantin Rausch fired the visitors into the lead in the 31st minute and Mohammed Abdellaoue doubled it after the break as Schalke's once mighty defence was a shadow of its former self.
Jermaine Jones pulled one back with a well-taken header eight minutes from time but the hosts, runners-up last season, were unable to find the equaliser and will have to wait longer for their first points this season.
Schalke's defeat was preceded on Friday by another surprise when champions Bayern Munich lost 2-0 at promoted Kaiserslautern with the hosts netting both goals in 60 seconds.
Kaiserslautern and Hoffenheim, who beat St Pauli 1-0, are joint top with six points from two games, ahead on goal difference of Mainz, Hamburg and Hanover
Ruud van Nistelrooy scored his third goal in two matches as Hamburg SV beat Eintracht Frankfurt 3-1 while VfL Wolfsburg squandered a 3-0 lead to lose 4-3 to visitors Mainz.
Bosnian Edin Dzeko scored twice and new Brazilian signing Diego added another to give the 2009 champions a huge lead but Mainz pulled one back before the break and added two more early in the second half before Adam Szalai grabbed the winner six minutes from time.
"It is really hard to explain what happened today," said Wolfsburg coach Steve McClaren, whose team are still without a point after also losing their opener to Bayern Munich last week.
"I have never seen such a dramatic loss of quality," said the former England manager.
Werder Bremen, buoyed up by their Champions League group stage qualification in midweek, demolished Cologne 4-2.
WEAK DEFENCE
Schalke were desperate to make amends after losing their opener to Hamburg but found it hard going against a tight Hanover defence.
Their own backline was shaky, allowing Hanover striker Didier Ya Konan to take stabs at it with Schalke still unable to fill the void left by the departure of versatile defenders Heiko Westermann and Rafinha as well as Marcelo Bordon.
Hanover gradually became bolder and grabbed the lead through Rausch's solo effort. The visitors then came close to a second goal minutes later when Moritz Stoppelkamp managed to fire wide from five metres and he hit the post seconds later.
"We became very insecure after the first goal," said Schalke coach Felix Magath, who is at odds with the club's fans after sacking their representative on the board. "But I still believe we can solve our problems."
Abdellaoue, the Norwegian forward who joined earlier this month, was on target for their second goal after a beautiful through ball from Manuel Schiedebach that left the Schalke defence frozen.
Jones cut the deficit late in the game but it looked more likely that Schalke that would concede another rather than level, with Hanover missing three clear chances on the break in the dying minutes.
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