Bayern looked on course for their seventh straight Bundesliga win after striker Eric-Maxim Choupo-Moting scored in the 37th minute, but Halstenberg levelled in the 52nd minute.
Veteran Bayern forward Thomas Mueller had a chance to win the match in injury time with a shot from point blank range, but dragged his effort just wide.
A combination of rustiness after a ten-week break and sub-zero temperatures meant both sides struggled to find rhythm early on.
Central defender Josko Gvardiol, one of the breakout stars at the World Cup, almost scored an own goal after seven minutes, when his attempt at smothering a Serge Gnabry cross hit the post.
Bayern midfielder Leon Goretzka headed the ball in the back of the net after 31 minutes, but the goal was struck off due to a narrow offside against Munich centre-back Matthijs de Ligt in the build up.
The reigning champions got on the board soon after through Cameroon striker Choupo-Moting, who tapped a Gnabry cross past the outstretched arm of Leipzig keeper Janis Blaswich to score his 11th goal in ten games in all competitions.
Leipzig shook off the cobwebs to reclaim parity shortly after halftime when Halstenberg side-footed in a Dominik Szoboszlai header to score his first goal of the season.
The goal sparked Leipzig's most dominant period of the game, with the home side frequently threatening Bayern on the counter as the visitors pushed to regain the lead.
Bayern were fortunate not to be reduced to ten men in the 66th minute when France defender Dayot Upamecano brought down a rampaging Szoboszlai who was through on goal with only goalkeeper Yann Sommer to beat.
Upamecano, one of four former Leipzig players in Bayern's squad along with manager Julian Nagelsmann, received a yellow card.
Leipzig will likely be the happier of the two sides with the result, but Bayern will still finish the round as outright table leaders, regardless of other results.
The Red Bull-owned side has now only managed to beat the Bavarians once in 16 competitive appearances since their promotion to the Bundesliga for the 2016-17 season.
With less than half of the season's fixtures played, Leipzig sit six points behind Bayern in third.
Second-placed Freiburg have a chance to cut the gap at the top to two points when they travel to Wolfsburg on Saturday.