The win, on a day when Jupp Heynckes clocked up the 1,000th Bundesliga appearance of his career as player and coach, took them a 18 points clear of Borussia Dortmund, who visit Borussia Moenchengladbach on Sunday.
Bayern, who beat Schalke 04 4-0 in their previous home game, have won 19 of their 23 league games, conceded only eight goals and inadvertently made a mockery of the Bundesliga's claim to be the most open and competitive in Europe.
Werder found themselves two goals behind and reduced to 10 men by halftime and Bayern found almost no resistance as they steamrollered their opponents in the second half.
Mario Gomez scored twice while Arjen Robben, Javi Martinez and Franck Ribery bagged one each with Theodor Gebre Selassie putting through his own net.
Ivorian striker Didier Ya Konan scored twice, including a spectacular volleyed effort, as he helped Hanover 96 beat Hamburg SV 5-1 at home to move up to seventh with 33 points, one behind their opponents.
Ya Konan collected a misplaced pass, flicked the ball up with his right foot and then produced a dipping 25-metre volley with his left.
Augsburg beat Hoffenheim 2-1 to move out of the bottom two, where they were replaced by their own opponents.
Goals from Ji Dong-won and Sascha Moelders left hosts Augsburg in 16th place, the relegation playoff spot.
VfL Wolfsburg managed a 1-1 draw at Mainz 05 despite having Alexander Madlung sent off in the 30th minute for a tackle from behind. Niki Zimling put Mainz ahead in the fifth minute and Naldo levelled 10 minutes later.
Central defender Joel Matip scored twice, including an 81st minute winner, to give Schalke 04 only their second win in six games under new coach Jens Keller as they beat Fortuna Duesseldorf 2-1 in Gelsenkirchen.
The 21-year-old Cameroon international, who opened the scoring just before the half hour, was left unmarked at the far post to turn in a mis-directed Michel Bastos shot to give ninth-placed Schalke a badly-needed win.
Heynckes, who made his Bundesliga debut as a player in August 1965, was still not satisfied with treble-chasing Bayern's efforts after his team conceded a league goal for the first time since the start of the year.
"It's annoying that we didn't keep another clean sheet," he told Sky Sports.
But he added: "My team did very well and scored some good goals. We want to maintain our rhythm, continue on our way, and not be put off by premature congratulations from anywhere. We go out seeking to play even better, more successful football."
Bremen coach Thomas Schaaf was under no illusions.
"We wanted to put up more resistance, but we were in no position to do so. We've been handed a nasty beating here today," he told reporters.
Bayern made six changes from the side which beat Arsenal 3-1 on Tuesday in the Champions League but it barely showed.
Werder held out for 25 minutes before Philipp Lahm crossed from the right and, with Bayern players queuing up in the middle, Robben beat his team mate Ribery to the ball to knock in from close range and claim the goal.
Bayern again had an abundance of players in scoring positions four minutes later when Robben floated in a free kick and Martinez rose to head in with Toni Kroos unmarked behind him just in case he missed.
It got worse for Werder when Sebastian Proedl tripped goal-bound Gomez just outside the area and was sent off for what is known in Germany as an "emergency brake" (Notbremse).
There was no respite after halftime as Gebre Selassie made a complete hash of his attempt to clear away a low Gomez cross. He swung with his right foot, missed and the ball hit his other leg and flew into the goal in the 48th minute.
Gomez tapped in the fifth three minutes later after Ribery lobbed the ball over.
Kevin De Bruyne side-footed one back just before the hour and Bayern briefly eased off before Ribery and Gomez added further goals in the last five minutes.
- Sports & Recreation
- Mario Gomez
- Franck Ribery