Marco Reus put Dortmund in front in the ninth minute with Pierre-Emerick Aubameyang doubling their lead early in the second half.
Aubameyang then added a third, allowing Dortmund to leapfrog their opponents in the table and celebrate a much-needed win.
Meanwhile, debutant Andre Schurrle inspired Wolfsburg to a 3-0 win over Hoffenheim??as the Wolves kept up the chase of Bundesliga leaders Bayern Munich.
The former Chelsea forward set up Bas Dost and Kevin De Bruyne to give Wolfsburg a commanding lead going into the interval.
Hoffenheim tried to mount a recovery in the second half, but Wolfsburg’s lead never really looked in any danger before De Bruyne added a third as the Wolves stayed within eight points of the summit.
Bayern Munich kept that eight-point advantage at the top of the league intact while sending Stuttgart to the bottom of the pile with a 2-0 win at the Mercedes-Benz Arena.
After struggling for much of the first half, Bayern gained the lead with their first shot of the game as Arjen Robben netted his 12th goal of the season just before the interval.
David Alaba curled in an eye-catching second early in the second half to hand Bayern their first win of 2015.
Elsewhere, Pal Dardai celebrated a winning start to life as coach of Hertha Berlin as they picked up a 2-0 victory at Mainz, while Paderborn stalled their slide towards the bottom three of the Bundesliga as they picked up a point with a 0-0 draw at Cologne.
In the evening kick-off, a Marcelo own goal and a Marcell Jansen strike gave Hamburg a 2-0 lead going into half-time against Hannover.
The visitors pulled a goal back through??Artur Sobiech in the second half but it was not enough to stop Josef Zinnbauer’s side picking up all three points.