A first-half header from Sebastien Prodl combined with a glorious volley from former Inter man Marko Arnautovic and a sharp strike from substitute Claudio Pizarro after the break earned Bremen their first win in the group.
Breakthrough: Sebastian Proedl (far left) celebrates after putting Werder Bremen in front against Inter
It could have been even more emphatic for the Germans who hit the post and the bar as they carved open the defending champions in the second half.
FC Copenhagen stormed into the knockout stage with a 3-1 defeat of Panathinaikos apart at the Parken.
Great Danes: Jesper Gronkjaer (left) and William Kvist celebrate FC Copenhagen's qualification for the knockout stages
Martin Vingaard put the hosts ahead in the 26th minute and from then on they were dominant, with a 50th-minute penalty from Jesper Gronkjaer and Djibril Cisse's own goal wrapping up the points, before Cedric Kante netted late on for Pana.
The result ensured Copenhagen advanced from Group D in second place, though Barcelona's win over Rubin Kazan meant they would have gone through regardless.
A largely second-string Barca consigned Rubin to a place in the Europa League after securing a 2-0 win at the Nou Camp.
Andreu Fontas' deflected second-half effort and a late Victor Vazquez strike earned already-qualified Barca their fourth win in Group D.
Schalke secured top spot in Group B with a 2-1 victory away to hapless Benfica.Having already sealed their passage to the knockout stage thanks to a 3-0 win over Lyon a fortnight ago, goals by Jose Manuel Jurado and Benedikt Howedes, before Luisao's consolation, gave them the win required to qualify as winners.
Benfica made the Europa League anyway after Hapoel Tel Aviv succumbed to a late Alexandre Lacazette equaliser to draw 2-2 with Lyon.
After an entertaining but goalless first half Lisandro Lopez and Ben Sahar traded goals within a minute of each other around the hour mark before Eran Zahavi made it 2-1 to the visitors.
That would have been enough for third place and a parachute into the last 32 of the Europa League, but Lacazette popped up late on.
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Explore more:People: Marko Arnautovic, Claudio Pizarro, Ben Sahar Places: Copenhagen, Lyon, Barcelona