Eric Maxim Choupo-Moting's opener was his 12th goal of the season, his highest tally in a campaign in his career
Leaders Bayern Munich were held by Leipzig as the Bundesliga returned following a 68-day mid-season break.
Serge Gnabry hit the post and Leon Goretzka had a goal disallowed for an offside in the build-up.
Bayern got the first Bundesliga goal since the World Cup when Eric Maxim Choupo-Moting swept in Gnabry's cross from close range.
But third-placed Leipzig rescued a point when Marcel Halstenberg poked in from Dominik Szoboszlai's header.
Thomas Muller almost won the game for champions Bayern - who had won their previous 10 games - in injury time, but drove just wide from 20 yards.
They lead Freiburg by five points at the top of the league. Leipzig are one point further behind.
The Bundesliga, which broke up on 13 November, is the last of Europe's major leagues to return after the World Cup.
Veteran goalkeeper Yann Sommer made his Bayern Munich debut following his £8.3m move from Borussia Monchengladbach.
Bayern's first choice Manuel Neuer is out for the rest of the season after breaking his leg while skiing following Germany's early World Cup exit.
- Line-upsMatch StatsLive Text
Line-upsRB Leipzig
Formation 4-2-3-1
21Blaswich2Simakan4Orbán32Gvardiol23Halstenberg27Laimer24Schlager17Szoboszlai10Forsberg7Olmo19André Silva
- 21Blaswich2SimakanSubstituted forKlostermannat 83'minutes4Orbán32Gvardiol23HalstenbergSubstituted forRaumat 90+1'minutes27LaimerBooked at 71mins24SchlagerBooked at 41mins17Szoboszlai10ForsbergSubstituted forWernerat 67'minutes7OlmoSubstituted forHaidaraat 82'minutes19André Silva
Substitutes
- 8Haidara9Poulsen11Werner13Nyland16Klostermann22Raum37Diallo39Henrichs44Kampl
Bayern Munich
Formation 4-2-3-1
27Sommer5Pavard2Upamecano4de Ligt19Davies6Kimmich8Goretzka10Sané42Musiala7Gnabry13Choupo-Moting
- 27Sommer5Pavard2UpamecanoBooked at 66mins4de Ligt19Davies6Kimmich8GoretzkaBooked at 52mins10Sané42MusialaBooked at 35minsSubstituted forComanat 68'minutes7GnabrySubstituted forMüllerat 83'minutes13Choupo-MotingSubstituted forTelat 85'minutes
Substitutes
- 11Coman14Wanner18Sabitzer23Blind25Müller26Ulreich38Gravenberch39Tel44Stanisic
Referee:Daniel SiebertAttendance:47,069Match StatsHome TeamRB LeipzigAway TeamBayern MunichPossessionHome41%Away59%ShotsHome10Away7Shots on TargetHome3Away2CornersHome3Away2FoulsHome17Away12Live Text Post update
Match ends, RB Leipzig 1, FC Bayern München 1.
90'+5'Full Time
Second Half ends, RB Leipzig 1, FC Bayern München 1.
90'+4'Post update
Attempt blocked. Leroy Sané (FC Bayern München) left footed shot from outside the box is blocked. Assisted by Mathys Tel.
90'+3'Post update
Attempt missed. Thomas Müller (FC Bayern München) left footed shot from the centre of the box is close, but misses to the right.
90'+2'Post update
Attempt missed. Konrad Laimer (RB Leipzig) left footed shot from the left side of the box is just a bit too high. Assisted by Josko Gvardiol.
90'+2'Post update
Attempt blocked. Konrad Laimer (RB Leipzig) right footed shot from outside the box is blocked.
90'+1'Substitution
Substitution, RB Leipzig. David Raum replaces Marcel Halstenberg.
90'+1'Post update
Foul by Kingsley Coman (FC Bayern München).
90'+1'Post update
Xaver Schlager (RB Leipzig) wins a free kick on the right wing.
87'Post update
Attempt saved. Matthijs de Ligt (FC Bayern München) header from the right side of the box is saved in the top right corner. Assisted by Joshua Kimmich.
86'Post update
Leroy Sané (FC Bayern München) wins a free kick in the attacking half.
86'Post update
Foul by Xaver Schlager (RB Leipzig).
86'Post update
Foul by Mathys Tel (FC Bayern München).
86'Post update
Janis Blaswich (RB Leipzig) wins a free kick in the defensive half.
85'Substitution
Substitution, FC Bayern München. Mathys Tel replaces Eric Choupo-Moting.
84'Post update
Attempt missed. Timo Werner (RB Leipzig) left footed shot from the left side of the box is high and wide to the left. Assisted by André Silva.
83'Post update
Matthijs de Ligt (FC Bayern München) wins a free kick in the defensive half.
83'Post update
Foul by André Silva (RB Leipzig).
83'Substitution
Substitution, FC Bayern München. Thomas Müller replaces Serge Gnabry.
83'Substitution
Substitution, RB Leipzig. Lukas Klostermann replaces Mohamed Simakan.
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Source: bbc.com