It was the ninth consecutive victory for Dortmund in all competitions this season and showed they had put last season's disappointing performances behind them.
Manchester City defender Jerome Boateng has agreed to join Bayern Munich for four years but the English club have not yet agreed the deal, the player said on Tuesday.
Second-placed Bayern dropped nine points behind Werder with 14 games remaining.
Bayern Munich made predictably light work of Asian champions Guangzhou Evergrande, dispatching the Chinese side 3-0 in their Club World Cup semi-final and hitting the woodwork five times on Tuesday.
Champions Bayern Munich opened up an eight-point lead in the Bundesliga at the start of the German season's one-month winter break by beating Hanover 96 1-0 on Saturday amid mounting speculation over the future of coach Pep Guardiola.
Undefeated Bayern Munich stumbled to a 0-0 draw at Borussia Moenchengladbach on Sunday that ended a four-game winning streak in the league but they remain four points clear at the top.
Treble winners Bayern Munich edged past Eintracht Frankfurt 1-0 courtesy of a Mario Mandzukic volley on Saturday to equal their club record of 27 games without defeat as minnows Hoffenheim demolished Hamburg SV 5-1.
Bayern Munich's Robert Lewandowski and Arjen Robben scored twice each as the champions crushed Hanover 96 4-0 in the Bundesliga on Saturday to go four points clear at the top of the table as rivals Borussia Dortmund lost to Hamburg SV.
Bayern Munich showed no signs of letting up as they routed Eintracht Frankfurt 5-0 on Sunday for their 10th straight home win of the season in the Bundesliga.
Struggling Bolton Wanderers held European soccer aristocrats Bayern Munich to a 2-2 draw in UEFA Cup Group F on Thursday.
Bayern Munich tore Juventus apart on a rare off night for Andrea Pirlo and Gianluigi Buffon but had to settle for a 2-0 win after missing a hatful of chances in Tuesday's Champions League quarter-final first leg.
Bayern Munich defeated Kaiserslautern 3-1 in the German Cup final for their fourth domestic league and cup double.
Manchester United remain very dangerous opponents despite their struggles domestically as they focus their efforts on Europe, Bayern Munich coach Pep Guardiola said on the eve of their Champions League quarter-final first leg.
Bayern Munich midfielder Thiago Alcantara will be out of action until early November after having surgery on Monday for damaged ligaments, the club said.
New coach Pep Guardiola shuffled the cards at Bayern Munich as the treble winners beat his former club Barcelona 2-0 in a friendly on Wednesday.
Manchester United bolstered their squad with a flurry of transfer deadline day signings, Manchester City and Liverpool also splashed out while ambitious Brighton & Hove Albion sealed an audacious loan deal for Barcelona's Ansu Fati on Friday.
Bayern Munich have appointed former Barcelona coach Pep Guardiola to replace Jupp Heynckes from the end of this season, the Bundesliga club said on Wednesday.
In other matches, VfL Wolfsburg edged past Hertha Berlin 2-0; promoted Ingolstadt snatched a last-gasp 1-0 win at Werder Bremen
Bayern Munich were held to a 2-2 draw by Aberdeen, while Atletico Madrid lost 1-0 at Bolton Wanderers in the UEFA Cup last 32 first-leg matches.
Kane was confirmed as a Bayern Munich player on Saturday after weeks of wrangling between the clubs.
Bayern Munich beat VfB Stuttgart 4-1 on Sunday to move 12 points clear in the Bundesliga with only one point required from their last four games to seal a 21st German title. Luca Toni scored his 36th goal in 42 matches in the eighth minute. Antonio da Silva equalised nine minutes later before Mark van Bommel fired in a superb low shot that curled around the wall off an indirect free kick in the 55th minute.
Now only Inter stand in the way of a treble that would match Manchester United's still unique feat of 1999.
Manchester City manager Pep Guardiola believes Bayern Munich and Barcelona would have sacked him if he had overseen a similar campaign to the one his Manchester City team have had at either of the European powerhouses.
Manchester United's lead in England was cut to three points when they could only play out a 2-2 draw against Middlesbrough while Chelsea won 2-0 at Manchester City. A round-up of weekend action in the main European leagues.
Bayern Munich humiliated former Bundesliga powerhouses Werder Bremen 7-0 on Saturday with Franck Ribery scoring twice and setting up another two as the champions kept up their seemingly unstoppable march towards another title.
Champions Borussia Dortmund closed in on their second consecutive Bundesliga title on Wednesday, beating rivals Bayern Munich 1-0 with a backheel from Robert Lewandowski to go six points clear at the top of the table with four games left.
Italy striker Luca Toni scored twice to steer Bundesliga leaders Bayern Munich to a 2-1 victory over Bayer Leverkusen on Saturday.
Bundesliga leaders Bayern Munich survived several first-half scares in a 1-1 home draw with midtable Schalke 04 on Saturday as Philipp Lahm made his 500th appearance for the Bavarian club.
The All India Football Federation on Monday gave the green signal for the May 27 exhibition tie between Mohun Bagan and German giants Bayern Munich in Kolkata, but refused to release the Bagan players called for national duty.
Formula One boss Bernie Ecclestone said he would fight a $400 million damages claim that German bank BayernLB is planning to file in London over the sale of the motor racing business in 2005.
Striker Mario Gomez pounced from close range in the final minute to give Bayern Munich a 2-1 victory over Real Madrid in the first leg of their Champions League semi-final on Tuesday.
Bayern Munich's Franck Ribery was sent off for slapping an opponent just after halftime but that did not stop his side moving into the German Cup quarter-finals with a 2-0 win at Augsburg on Tuesday.
Title holders Bayern Munich eased into the second round of the German Cup with a comfortable 4-0 win over amateurs Germania Windeck on Monday, with striker Miroslav Klose scoring once and setting up another goal.
Lionel Messi was in inspired form as champions Barcelona hammered Celta Vigo 5-0 on Saturday, recording a fourth straight league victory which keeps them top of La Liga after Real Madrid had put the pressure on the Catalans with a 4-1 win at Eibar.
Substitute Toni Kroos hit a last-gasp winner as four-times European champions Bayern Munich came from behind to win 3-2 at Red Star Belgrade in the UEFA Cup.
Bayern Munich will not release France forward Franck Ribery for a disciplinary hearing by the French Football Federation to probe his alleged role in the team's World Cup revolt, the German champions said on Monday.
After damaging losses to Dinamo Zagreb and Olympiakos Piraeus in their first two fixtures, the Gunners have to win to advance to the knock-out stages
Manchester United took over at the top of the Premier League while Barcelona's Argentine forward Lionel Messi could be out for up to two months with a knee injury and rampant Bayern Munich extended their perfect start to seven league wins.
Bayern Munich made it seven wins out of seven in the Bundesliga on Saturday as two goals from Franck Ribery led them to a 2-0 win over a toothless Hoffenheim in an embarrassingly one-sided match.
Barcelona extended their LaLiga lead to eight points thanks to second-half goals by Jordi Alba, Gavi and Raphinha that gave them a 3-0 home win against Sevilla