Bayern started slowly and fell behind after only 65 seconds to Marcel Sabitzer's header from a rapid counterattack.
Thiago Alcantara pulled one back for Bayern, but the visitors' defense was again made to look poor when Werner scored his second - this time through Tom Starke's legs from a hard angle.
Bayern drew level when a Lahm cross clipped the arm of defender Bernardo and Lewandowski drilled home the penalty on 16 minutes.
And then Arjen Robben waltzed his way through the Leipzig defence before firing home a trademark left-foot finish to crown an unbelievable Bayern fightback with virtually the last kick of the match.
But Ancelotti, who has led Bayern to the Bundesliga title in his first season in charge at the Allianz Arena, was quick to dismiss such claims.
"It's a dream game for us and we have nothing to lose".
WWE SmackDown Results: Biggest Winners, Losers and Moments from May 9
Sami Zayn and Baron Corbin have been feuding for a few weeks, but there is no official match scheduled for them to fight it out. Ahead of their highly anticipated arrival, The New Day declares that the rest of SmackDown LIVE's tag teams are booty.
Reports in the French media suggested that Ribery has been at odds with Ancelotti in recent months, including a disagreement during the return leg of their Champions League quarter-final tie with Real Madrid. "We could have a really cracking game", he added.
Bayern substitute Thomas Muller echoed his captain's sentiment, saying: "We badly wanted it and showed great morale". "Leipzig have absolutely deserved to be where they are now".
"It was a insane game and as expected, it was very open", said Ancelotti.
"For the spectators it was certainly a nice game to watch - but not for us".
Leipzig coach Ralph Hasenhuettl says his team have nothing to lose at home against Bayern's stars. There was some very attacking football.
"Therefore Bayern Munich wish Holger Badstuber all the best and we thank him for his exemplary commitment in almost 15 years at Saebener Strasse (Bayern's training ground)".
U.S. dollar, yields rise; stocks slip from record highs
Declining issues outnumbered advancing ones on the NYSE by a 1.23-to-1 ratio; on Nasdaq, a 1.22-to-1 ratio favored decliners. The last time the VIX touched a level this low, it was 1993 and Sleepless in Seattle was about to hit movie house marquees.
"Leipzig have been a fantastic rival this season".
And Leipzig - who ran them pretty close at one point earlier in the year - remain second in the table, but a whole 13 points behind their lofty opponents.
To further highlight just how good Bayern usually are at the back, the four goals they conceded today against Leipzig accounts for 19% of the goals they have conceded in the league this season. They have some young players and are very motivated.
"Both teams played great football, but could have defended better".
After six seasons with Bayern, it seems Boateng may be looking for a new challenge as he looks for the Die Roten board to clarify his position in the team so he can assess his situation ahead of the summer transfer window.
Hertz Global Holdings, Inc (NYSE:HTZ) Sale Analysis
Zacks Investment Research raised Hertz Global Holdings from a "sell" rating to a "hold" rating in a report on Monday, May 1st. Finally, Credit Agricole S A purchased a new position in Hertz Global Holdings during the fourth quarter valued at $341,000.