Bayern warmed up for Tuesday’s Champions League clash at AS Roma by maintaining their four-point lead at the top of the table, boosting their goal difference to plus 19 as former Germany captain Philipp Lahm and Mario Geotze scored twice.
Lahm started the rout when he crashed his shot home from 14 metres out with 20 minutes gone at Munich’s Allianz Arena.
Alonso, who joined Bayern from Real Madrid in August, netted his first goal for the club when he drove a free-kick under the Bremen wall on 27 minutes.
Thomas Mueller put the hosts 3-0 up when he converted a penalty after being dragged down in the area by Bremen’s Sebastian Proedl on 43 minutes.
And Goetze made it 4-0 at the break when he held off Congo defender Assani Lukimya to bury his shot in the far corner.
Lahm and Goetze both added their second goals as the hosts profited from a tiring defence in the final 20 minutes and the result left Bremen bottom of the table.
With Hoffenheim at Hamburg on Sunday, Borussia Moenchengladbach went second in the table with a 3-0 win at Hanover 96 as Germany squad member Max Kruse scored twice and Swiss midfielder Granit Xhaka netted a free-kick.
– Dortmund beaten again –
However, Borussia Dortmund’s horror league run continued as they lost 2-1 at Cologne to make it five Bundesliga games without a win, and their third defeat in a row, ahead of Wednesday’s Champions League clash at Galatasaray.
Dortmund’s Germany midfielders Ilkay Gundogan — who had been out for more than a year — and Marco Reus returned from injury, but were powerless to stop Cologne taking a 1-0 lead as midfielder Kevin Vogt fired home on 40 minutes.
Dortmund’s Italy striker Ciro Immobile equalised, but Cologne’s Simon Zoller netted the hosts’ winner on 74 minutes to seal their first win at home against Borussia since 2003.
The result sees Dortmund drop to 14th in the table — just two points above the bottom three — while Cologne are 10th.
Bayer Leverkusen, who host Zenit St Petersburg in the Champions League on Wednesday, threw away a three-goal lead in their 3-3 draw at plucky VfB Stuttgart.
A win would have seen Leverkusen go third, but the draw saw them drop to sixth in the table.
Leverkusen raced into a 2-0 lead after only nine minutes as South Korea’s Son Heung-Min scored twice and could have had a hat-trick on 11 minutes when his lob hit the crossbar.
Germany’s Karim Bellarabi made it 3-0 just before the break when he converted Son’s pass to leave Leverkusen in full control.
But Stuttgart battled back as midfielder Timo Werner and left-back Florian Klein scored second-half goals before Martin Harnik headed Stuttgart level on 76 minutes when he was left unmarked at the far post — by Son.
VfL Wolfsburg went third with a 2-1 win at Freiburg as midfielder Daniel Caligiuri scored twice against his old club, while Mainz went fourth after their 2-1 win at home to Augsburg.
Ex-Chelsea manager Roberto di Matteo makes his debut as Schalke 04 coach later when the 12th-placed Royal Blues host Hertha Berlin in a mid-table clash.