Werder were undone by three goals from counter-attacks and a David Alaba free kick but did enough to rile the visitors to the point that defender Jerome Boateng, one of six players booked, became involved in an argument with a ball boy.
Runaway leaders Bayern, who have 64 points from 25 games, are now 14 clear of second-placed VfL Wolfsburg who host Freiburg on Sunday (1430 GMT).
Joel Matip scored a last-minute equaliser as visiting Schalke 04 twice came from behind to hold Hertha Berlin 2-2 while Anis Ben-Hatira was booked for putting on a spider man mask as he celebrated the opening goal for the hosts.
Eintracht Frankfurt brushed past Paderborn 4-0 and Hamburg SV are hovering just above the relegation zone after having goalkeeper Jaroslav Drobny sent off in the 19th minute during a 3-0 defeat at Hoffenheim.
Eugen Polanski converted a penalty following Drobny's foul and later added a second as Hamburg were left in 15th, one place and two points clear of Paderborn who are in the relegation playoff spot.
Bayern, who have scored 34 goals in their last eight games in all competitions and thumped Werder 6-0 earlier in the season, went ahead in the 24th minute when Thomas Mueller curled the ball in from the edge of the area following a counter-attack.
GOAL DISALLOWED
Despite missing Franck Ribery and Arjen Robben through injury, the leaders were as clinical as ever and Alaba chipped in a free kick in the last minute of the first half to make it 2-0.
Werder had a goal disallowed for handball in the second half and the game turned ugly with several late tackles and heated exchanges between the players.
Almost inevitably Werder were caught on the break when Lewandowski grabbed two goals in the final quarter of an hour, both set up by Mueller after lightning attacks.
Bundesliga top-scorer Alexander Meier took his tally to 19 this season as he set Eintracht on the way to an easy win. Marc Stendera, Stefan Aigner and Nelson Haedo were also on target.
Schalke followed up their 4-3 Champions League second leg win at Real Madrid in midweek with another dramatic game.
Ben-Hatira opened the scoring for Hertha, prodding home a rebound, but they were pegged back before halftime when 19-year-old Leroy Sane dinked the ball over Thomas Kraft.
Genki Haraguchi put Hertha back in front with nine minutes left only for Matip to head in for Schalke.
(Writing by Brian Homewood, editing by Tony Jimenez)
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