Goals from Shinji Kagawa, Pierre-Emerick Aubameyang and Christian Pulisic helped lift them onto 13 points and set a club record of keeping five consecutive clean sheets at the start of the season.
"When the team again keeps a clean sheet and then scores three goals as well then I can only be proud of them," Dortmund coach Peter Bosz told reporters.
"We had chances in the first half to score a second goal. If we had done that at that point it would have been easier. It was a very tough game, maybe the toughest so far."
Dortmund's speed in attack was always going to be a problem for the hosts and American Pulisic almost put the visitors ahead early on.
Last season's top Bundesliga scorer Aubameyang then headed on to the post from a Andriy Yarmolenko cross before Japan international Kagawa slotted in from close range in the 25th.
Aubameyang got on the score sheet in the 63rd, finishing off a quick Dortmund break and he should have scored another when he had only keeper Christian Mathenia to beat in the 74th.
Pulisic made sure of the three points five minutes later with his shot going in off the post.
Dortmund are a point ahead of Bayern Munich after the champions' 3-0 win at Schalke 04 on Tuesday.
Hoffenheim climbed to third, on 11, after recovering from a two-goal deficit to snatch a 3-2 stoppage-time win at Mainz 05 thanks to Mark Uth's late winner
Hanover 96 failed to keep pace and dropped to fourth also on 11 after their 1-1 draw at Freiburg, who earned a point thanks to substitute Nils Petersen.
Super sub Petersen extended his league record of scoring as a substitute with his 20th goal after coming on.
Cologne made it five losses in a row, their worst Bundesliga start in the club's history, after their 1-0 defeat to Eintracht Frankfurt.
Cologne, however, were left fuming after claiming the video assistant referee should not have agreed with a decision to award Eintracht's winning penalty.
The club had already been let down by the VAR last week in their 5-0 loss to Dortmund and had briefly considered appealing for a rematch.
(Reporting by Karolos Grohmann; Editing by Toby Davis)
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