Bundesliga: Eintracht Frankfurt 2 Hannover 3
Tayfun Korkut's men flew out of the blocks as Leon Andreasen headed home Christian Pander's cross to give them a second-minute lead.
Frankfurt pulled level with 13 minutes gone, though, as Martin Lanig on the end of a wonderfully delivered Tranquillo Barnetta free-kick that caught the Hannover defence napping.
A pulsating first half continued as midfielder Lars Stindl nodded home his second goal in as many games to restore the visitors' advantage after Pander once again supplied the ammunition.
Hannover striker Ya Konan added a third just before the half-hour mark, collecting a precision pass from Andreasen and coolly slotting beyond Kevin Trapp in the Frankfurt goal.
Andreasen and Szabolcs Huszti hit post and bar respectively as Hannover threatened to run riot but they were left hanging on after Alexander Meier powered home to set up a grandstand finish.
The result moves Hannover level on points with their hosts and eight points above the bottom three.