Bremen captain Frank Baumann scored an own goal in the 59th, when he tried to kick the ball out of play, to bring about his team's first loss this season.
Manchester United forward Wayne Rooney will miss the next two Champions League matches after being sent off at Villarreal last week.
UEFA said Tuesday that the 19-year-old England international will be absent when Manchester United hosts Benfica on Sept. 27 and at Old Trafford against Lille on Oct. 18.
Rooney received his second yellow card in last Wednesday's 0-0 draw at Villarreal when he sarcastically applauded in referee Kim Milton Nielsen's face after being booked for tripping an opponent.
The referee also reported in his post-match report that Rooney swore at him as he left the field.
In statements to UEFA on Tuesday, Manchester United and Rooney admitted the player's reaction in clapping his hands was wrong. However, UEFA said they contested whether there was subsequent verbal abuse of the referee.
UEFA said Manchester United have until midnight Friday to appeal the decision.
Rooney is already suspended for England's next World Cup qualifying game against Austria on Oct. 8 after receiving a yellow card against Northern Ireland earlier this month.