A 61st-minute Hiroshi Kiyotake free-kick sealed Hannover's first victory at Signal Iduna Park since April 2008, increasing the heat on Dortmund coach Jurgen Klopp as a result.
The home side crafted numerous opportunities in a one-sided first period, with Mats Hummels seeing his header tipped onto the frame of the goal by Ron-Robert Zieler.
Dortmund's pressure continued early in the second half, with Marco Reus wasting numerous chances before Kiyotake curled in to claim an unlikely victory.
Ceyhun Gulselam was dismissed in the dying stages for Hannover, but the visitors held on.
The win ends Hannover's run of three consecutive league losses and ensured Dortmund succumbed to a fifth defeat in their last six Bundesliga fixtures, with Klopp's men still unable to replicate their fine UEFA Champions League form domestically.
Stuttgart and Eintracht Frankfurt shared nine-goals in a thriller at Commerzbank-Arena, Armin Veh's visitors prevailing 5-4.
Alexander Madlung gave Frankfurt the lead in the 21st minute, only for Stuttgart to take control of proceedings and eventually go 3-1 up early in the second half, Christian Gentner and a Martin Harnik double doing the damage.
Frankfurt battled back, though, and they looked destined to steal victory as three goals in eight minutes from Alex Meier, Stefan Aigner and Madlung giving Thomas Schaaf's men a 4-3 lead.
Stuttgart, however, were not finished and they snatched victory in the final ten minutes thanks to goals from Timo Werner and Gentner, with Haris Seferovic's 86th-minute sending off effectively ending Frankfurt's hopes of a victory.
Like their bitter rivals Dortmund, Schalke's inconsistent run continued on Saturday as they were beaten 1-0 at Bayer Leverkusen, who themselves stay fourth.
Hakan Calhanoglu netted the only goal of the game with a fine free-kick in the 53rd minute and, although Tin Jedvaj earned a red card for a crude challenge on Jan Kirchoff towards the end, Leverkusen held on for all three points.
Hoffenheim's continued their unbeaten start to the Bundesliga season with a 1-0 win over Paderborn, moving themselves up to second ahead of Borussia Monchengladbach, who host pacesetters Bayern Munich on Sunday.
A double from Anis Ben-Hatira helped Hertha Berlin to a comfortable 3-0 win over struggling Hamburg, while Freiburg remain winless after losing 2-0 at Augsburg.
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