It could have been a different story had they built on Niclas Fuellkrug's opener, but Timo Roettger and Carsten Kammlott completed the comeback for the home side.
Joseph Akpala hit the crossbar early on for Bremen as the Bundesliga side made a strong start.
And they were rewarded in the 13th minute when Marko Arnautovic weighted a wonderful pass to Fuellkrug, who duly applied the finish.
Werder were unable to build on that advantage, though, and they were pegged back on the stroke of half-time, as Roettger showed neat foot work in the area to dribble his way through the defence and fire into the top corner.
Tim Sebastian came close to making it 2-1 for Leipzig in the 58th minute, but they did not have to wait long for their second goal as just a minute later, Denis Thomalla played a teasing ball into the box and Kammlott made no mistake with the finish.
There was almost a third for the home side when Yussuf Poulsen was denied by a smart save from Sebastian Mielitz in the Bremen goal.
But it made no difference, as Leipzig held on for victory.
