Dortmund earned their third straight league win of the new season as Poland striker Robert Lewandowski showed why Borussia recently raised his wages from a reported €20,000 to 60,000 ($80,286) per week for the last 10 months of his contract with the winning goal.
Lewandowski celebrated his 101st Bundesliga appearance when he converted Marco Reus's cross from the right in the 55th minute to claim the three points.
"I had a lot of chances and we're happy that we won, but we have to improve our game, 1-0 at home is not enough," admitted Lewandowski, who turned 25 on Wednesday.
With reigning European champions Bayern Munich, who are joint second with Bayer Leverkusen, hosting Nuremberg on Saturday, Dortmund's win at the Westfalenstadion leaves them three points clear with a goal difference of six
compared to Bayern and Leverkusen's three.
"In a way it was good that we didn't score earlier, because it would have taken some of the fire out of the players," said Dortmund coach Jurgen Klopp.
"This way, they had their feet on the gas for the whole 90 minutes. Having nine points after only three games and talking about how we can improve is almost a luxury problem."
This was Bremen's first league defeat of the season, and their first under new coach Robin Dutt, after they saw off promoted Eintracht Braunschweig and
Augsburg on the first two weekends.
The result was rarely in doubt as Dortmund dominated from start to finish with the hosts spraying the visitors' goal with 32 shots -- 16 on target -- compared to Bremen's seven, only four of which troubled Dortmund goalkeeper Roman Weidenfeller.
Dortmund enjoyed around 60 percent possession for the majority of the 90 minutes, while Germany star Reus was a constant thorn in the Bremen defence from the left wing and Lewandowski could have finished with a hat-trick.
The Poland striker forced Bremen goalkeeper Sebastian Mielitz into first-half heroics, twice denying him from close-range, while his compatriot Jakub Blaszczykowski rattled the Bremen crossbar on 36 minutes with Mielitz beaten.
At the other end Bremen striker Marko Arnautovic, who recently turned down a move to Scottish champions Celtic, was limited to half chances as he started for the first time since being suspended by the club in April after being stopped by police for speeding.