Teenage substitute MarkoMarin tested Carson from long range in the 75th minute, then Wiese tipped Wright-Phillips' fierce effort onto the outside of his left-hand post four minutes later.
The home side were fortunate not to be reduced to ten men on four minutes when MarkoMarin threw himself into a wild and dangerous challenge on Stephane Mbia.
Stanislav Sestak put the visitors ahead inside the first minute but Bremen hit back with first-half goals from Aaron Hunt and MarkoMarin, while Tim Borowski and Mesut Oezil netted after the break.