Bundesliga: Borussia Dortmund 1 Hoffenheim 0
Jurgen Klopp's men have endured a torrid start to the domestic season and came into the clash at Signal Iduna Park propping up the rest of the division.
Dortmund were the better side throughout much of the encounter and sealed victory courtesy of Ilkay Gundogan's first-half header.
For Gundogan, who recently returned after a long spell out with a back injury, it was a first goal for Dortmund since netting in the 4-2 win over Bayern Munich in the DFL Supercup in July 2013.
The hosts could have won by more and were wrongly denied a second goal when Pierre-Emerick Aubameyang saw a header incorrectly disallowed for offside shortly after half-time, while the Gabon international saw another effort chalked off by the officials in the final 20 minutes.
Hoffenheim had late appeals for a penalty waved away when substitute Tarik Elyounoussi went down after tangling with Neven Subotic, but Klopp's men held on to their slender lead to secure only their second victory in the past 11 league outings.
Dortmund made five changes from their 2-0 defeat at Eintracht Frankfurt last weekend and were ahead after 17 minutes through Gundogan following a bright start.
Aubameyang got away down the right-hand side and delivered a teasing cross that goalkeeper Oliver Baumann came for but failed to get a touch on, allowing Gundogan to net with a flying header.
Sven Schipplock, who had been a doubt for the game with a groin problem, snatched an effort wide from 20 yards in the 37th minute as Hoffenheim went in search of an equaliser.
The visitors almost found one two minutes into the second period, but Mats Hummels was alert enough to run back towards his own goal and clear Sebastian Rudy's free-kick away from danger.
Dortmund should have seen their advantage doubled shortly afterwards, but, after Aubameyang nodded in Sebastian Kehl's flick-on at the far post, the linesman raised his flag to signal offside, with replays showing that to be the incorrect decision.
Aubameyang had the chance to render that injustice irrelevant on the hour, but his low effort after bursting through the middle was kept out by the left foot of Baumann.
The Hoffenheim goalkeeper excelled himself again a minute later, reacting smartly to tip Hummels' powerful header over the crossbar.
Dortmund continued to dominate and Aubameyang was again denied by the linesman's flag in the 72nd minute, with replays this time proving it to be the tightest of calls.
Gundogan should have put the result beyond doubt when he volleyed over from 10 yards with seven minutes to go, and there were vociferous appeals from the Hoffenheim players three minutes later as they pleaded for a penalty after Elyounoussi tumbled under a challenge from Subotic.
Referee Felix Zwayer was unmoved, however, as Dortmund were able to cling on to a much-needed victory.