Bremen had kept clean sheets in their opening two Bundesliga games, and they looked capable of making that three until Robert Lewandowski broke the deadlock in the second half at the Signal Iduna Park.
Jakub Blaszczykowski crashed an effort against the crossbar and Marco Reus fired just wide in a frustrating first-half for the home side.
Nuri Sahin volleyed wide from Marcel Schmelzer’s cross, while Henrikh Mkhitaryan found himself on goal after a neat one-two with Lewandowski, but could only lift his effort over.
Reus was continually Dortmund’s biggest threat and went close after collecting Kehl’s cross-field ball, but could only fire an effort wide of Sebastian Mielitz’s far post.
After a dominant first-half display Dortmund finally breached the Bremen's defence in the 55th minute.
Kevin Grosskreutz’s short pass was collected by Reus in the box and he fired a ball hard along the six-yard box where Lewandowski was on hand to tap home.
The goal seemed to knock the wind out of Bremen's sails, and they were nearly two behind when Schmelzer's hanging cross was palmed away by Mielitz and Sahin hit an acrobatic scissor kick that sailed over.
Dortmund continued to press, and with seven minutes remaining Mats Hummels flicked on Reus' corner to Lewandowski but his effort was blocked on the line by Hunt.
Weidenfeller had to be alert late on, as he produced a smart save at the near post from substitute Franco Di Santo to preserve the points for Dortmund and send them top ahead of Saturday's action.
