Lewandowski leads BVB over Bremen
Lewandowski scored in the 55th minute. Marco Reus crossed from the right to give the Poland striker an easy finish from close range.
Dortmund, last season's Champions League runner-up, created numerous chances before that, but lacked the efficiency to turn them into goals.
''We need to look at it and see what we can do better. At the moment all I can say is that we didn't put the ball in. But there are reasons for that,'' Dortmund coach Juergen Klopp said.
Jakub Blaszczykowski rattled the crossbar in the first half, and Bremen captain Aaron Hunt twice cleared off the line.
''Something's still missing. We're not yet at 100 percent,'' said Marco Reus, who had eight efforts on goal alone.
Marko Arnautovic almost gave Bremen the lead before the break, when his low effort whizzed past the post in his side's only chance of the first half.
''We should have had more of these scenes,'' Bremen coach Robin Dutt said.
Dortmund substitute Pierre-Emerick Aubameyang had a chance to seal the win in the 75th, only to be denied in a one-on-one with Bremen goalkeeper Sebastian Mielitz.
Roman Weidenfeller then pulled off a good save to deny Bremen substitute Franco di Santo a late equalizer on the Argentine's Bundesliga debut.
Lewandowski's goal was the first Bremen conceded this season, in its third game. Dortmund maintained its perfect record.
The only previous two times when Dortmund started the season with three wins, the side went on to win the title in 2001-02 and 1994-95.