Jurgen Klopp's side were outstanding in Turkey on Wednesday, storming to a 3-0 lead by half-time in a game they never looked like losing.
Dortmund top Group D with three wins from as many matches and are already eight points ahead of both Anderlecht and Galatasaray.
That means qualification to the last 16 is almost guaranteed, but Europe has proved a welcome distraction for a Dortmund side struggling domestically.
Last season's second-placed finish seems a distant memory for Dortmund, who have lost five of their eight league matches to sit 14th - just one point above the relegation play-off spot.
But, when asked if the Istanbul win would be the trigger for a reverse in fortunes, defender Sokratis Papastathopoulos said: "This will show on Saturday against Hannover. But I think so.
"It is important that we finally stop [and] be compact in a game.
"If we win again... then we will have no problems in the future.
"I'm glad we finally [kept a clean sheet]. That was very important. We finally played again as Borussia Dortmund."
Dortmund are already 13 points behind unbeaten leaders Bayern Munich and have lost their last three in the league.
A 2-1 loss at Cologne on Saturday led Klopp to slam his side for being "so naive", but the recent injury returns of Marco Reus and Ilkay Gundogan are sure to strengthen Dortmund.
Reus showed his class with an assist and a goal in the Galatasaray win, while Pierre-Emerick Aubameyang netted twice as fellow striker Ciro Immobile was an unused substitute.
And Dortmund meet a Hannover side in equally poor form in the league, having lost four of their last five to undo their promising start.
The visitors have been struggling in front of goal, too, with only Hamburg having scored fewer than Hannover's meagre tally of five league goals in eight matches.
Tayfun Korkut needs more from strikers Joselu and Artur Sobiech, who have netted three of the five between them, if Hannover are to rise from their current position of 10th.
Dortmund will take confidence from their recent record against Hannover - they have won the last four in all competitions - while the visitors have also found it tough in defence in recent encounters between the two sides.
In their last 12 matches against Hannover, Dortmund have scored four goals or more on five occasions.
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