كتب : Mohamed Sabe
Early goals from Ronaldinho and Eidur Gudjohnsen secured the win for the European champions.
The result means Barcelona finish the group as runners-up with 11 points to join Chelsea, who beat Levski Sofia 2-0 in London, in the second round.
Bremen will have to settle for a UEFA Cup spot after slipping to third place.
Ronaldinho opened the score from a 13th minute free-kick that took a deflection before eluding goalkeeper Timo Wiese and finding the net.
The Catalan giants did not waste any time in securing their win as Ludovic Giuly sent an inch-perfect low cross to the unmarked Gudjohnsen who slotted home from close range in the 18th minute.
FIFA Player of the Year nominee displayed some magic in midfield and supplied his teammates several scoring opportunities that went to waste.
Bremen, eager to make the second round, pushed forward and had several chances to score but their efforts were kept at bay by Barca keeper Victor Valdes and his air-tight defense.
Elsewhere, Chelsea secured top spot in Group A after a comfortable win over Levski.
Andriy Shevchenko struck home the opener for the Blues when he latched on to a deft through pass from Frank Lampard in the 27th minute.
Substitute Shaun Wright-Phillips netted the second for Chelsea with seven minutes left to play after a neat pass from Ricardo Carvalho.