Champions League club Leipzig have now managed just one point from their last two league matches, having conceded five goals in them compared to nine goals in their first 14 matchdays.
Nordi Mukiele put the visitors, who were looking to bounce back from last week's defeat to Borussia Dortmund, ahead after five minutes but Wout Weghorst headed in the equaliser in the 22nd for his 11th goal of the campaign.
Both Angelino and Justin Kluivert came close late in the game to score a winner for Leipzig.
"The draw is in order though I think we did have the better chances to win it," Leipzig coach Julian Nagelsmann said. "We should have scored again. We just have to live with the one point."
Leipzig, who have won one of their last four league games, are on 32 points, with Bayern, in action against Freiburg on Sunday, on 33.