Dortmund, who have taken only one point in their last six league games, dominated the first hour but were foiled by Hanover goalkeeper Ron-Robert Zieler before Hiroshi Kiyotake curled in a delightful free kick against the run of play.
In complete contrast to the scrappy game in Dortmund, VfB Stuttgart squandered a 3-1 lead before bouncing back to beat Eintracht Frankfurt 5-4 in a nine-goal thriller to give coach Armin Veh a winning return to the Waldstadion.
Surprise package Hoffenheim overcame an early penalty miss by Sebastian Rudy as they stayed unbeaten and moved up to second. Kevin Volland's second-half goal gave them a 1-0 win over promoted Paderborn after both sides had hit the post.
Hakan Calhanoglu scored one of his trademark free kicks to give Bayer Leverkusen a 1-0 win overSchalke 04 who suffered their first defeat since Roberto Di Matteo replaced Jens Keller as coach.
Hertha Berlin piled on the misery for Hamburg SV, who are 16th, with a 3-0 win and Augsburg beat Freiburg 2-0 to leave their opponents winless.
After beating Galatasaray 4-0 away on Wednesday, Hanover seemed the ideal opponents to help Dortmund revive their domestic form, having lost their last three games.Dortmund's domestic form has been a baffling contrast to their performances in the Champions League where they have won all three games without conceding a goal.
Dortmund took control and the breakthrough seemed imminent as Zieler pushed Henrikh Mkhitaryan's low shot around the post and tippedMats Hummels' header onto the crossbar in the opening 20 minutes.
Marco Reus went agonisingly close either side of halftime yet was denied by Zieler, before Japanforward Kiyotake broke the deadlock at the other end in the 61st minute.
Dortmund lost their confidence, were frustrated by Hanover's spoiling tactics and never looked like equalising even after visiting defender Ceyhun Gulselam was sent off after a second booking late in the game
The Frankfurt epic began with Alexander Madlung firing the hosts ahead in the 21st minute before Austria forward Martin Harnik struck twice in three minutes to give the visitors a 2-1 halftime lead.
Christian Gentner added a third in the 51st minute only for Alex Meier, Stefan Aigner and Madlung to score in a nine-minute spell to put Eintracht 4-3 ahead.
Timo Werner levelled with eight minutes left before Gentner's goal two minutes later gave Stuttgart their second win of the season, leaving them 14th with nine points.
Stuttgart coach Veh was in charge of Eintracht for the previous three seasons, during which he led them back to the top flight.
Titleholders Bayern Munich, unbeaten leaders with 20 points, visit third-placed Borussia Moenchengladbach, on 16 points and also unbeaten, on Sunday (1630 GMT).