The Bavarian giants failed to impose themselves on their visitors early on in the game, creating the first clear-cut chance after 22 minutes when Mario Gomez's shot from six yards was deflected wide.
It was 2-0 to the league leaders just before the half-hour mark, this time Javi Martinez heading home Robben's free kick from inside 10 yards.
Things went from bad to worse for Bremen on the stroke of half time when Sebastian Prodl was sent off for bringing down Gomez inside his area just as the German striker was sent through on goal by Martinez.
Bayern went 3-0 up just four minutes after the break, Theodor Gebre Selassie putting the ball inside his own net in an attempt to clear a cross from Gomez.
Two minutes Gomez himself scored his side's fourth goal of the afternoon with a header from close range after some good work from Franck Ribery with the final pass.
However, Ribery made it 5-1 to Bayern on 86 minutes with a volley from the left side of the box and three minutes later Gomez scored his second goal of the afternoon when he turned in Robben's chip over the top of the Bremen defence.