Leipzig are three points behind Bayern in second, with Borussia Dortmund one point further back.
Leipzig's defence held firm to open the match amid wave after wave of attack led by Havertz, who eventually cut the ball back from the right flank for Leon Bailey to opening the scoring in the 30th minute.
It was the first time Leipzig - who came into the match with the stingiest defence in the Bundesliga - had conceded a goal in five games.
Leipzig struck back immediately however, with Roma loanee Patrick Schick heading in a lofted free kick from Christopher Nkunku to make it 1-1 in the 32nd minute. The goal, Schick's third in five games, survived a VAR check for handball.
Leverkusen striker Lucas Alario had a chance to make it 2-1 in the dying stages of the first half when he broke from the halfway line to find himself one-on-one with Leipzig keeper Peter Gulacsi, but hit his effort directly at the Hungarian shot-stopper.
The home side started the second half the better of the two teams, but were unable to capitalise on the creativity of Emil Forsberg, with talisman Timo Werner hooked in the 71st minute after having an off day.
Havertz, who had one final chance to snare all three points for Leverkusen in the 75th minute but was unable to control the ball with the goal beckoning, said he was disappointed not to get the win.
"When you look at the run of the match, it could've also been three points," Havertz said.
"In the first half, we weren't clinical enough in front of goal, but we had a good match overall."
Earlier, Wout Weghorst's late header helped Wolfsburg claw themselves back from two goals down to snatch a 2-2 draw at Union Berlin amid more protests against the German FA (DFB) and Hoffenheim benefactor Dietmar Hopp.
Dutch international Weghorst was a shining light for the visitors and would have had more goals to his name were it not for some excellent saves from Berlin keeper Rafal Gikiewicz.
In a dour first half punctuated by wind, heavy rain and fan protests, Union went 1-0 up in the 41st minute through Sebastian Andersson who headed in a superb set piece from Christopher Trimmel to chalk up his 10th goal of the year.
The match was then suspended for over 10 minutes during the first half when Union's hardcore ultras unfurled banners critical of the DFB as well as several targeting billionaire Hopp, who is reviled by German supporters due to his exemption from a rule that enforces fan control of teams via club member voting rights.
A day earlier similar protests targeting Hopp featured during Bayern Munich's 6-0 win at Hoffenheim.
Union players pleaded with home fans to remove the banners as the first half fizzled out.
They then came out for the second half with a bang, defender Marvin Friedrich heading in another set piece from Trimmel to score his first ever Bundesliga goal.
Wolfsburg didn't take long to hit back, however, with Yannick Gerhardt taking advantage of some sloppy defending to head the ball in unmarked and make the score 2-1.
With the clock winding down, Weghorst latched onto a cross from Joao Victor in the 81st minute to equalise, heading in to finally win his battle with Gikiewicz.
Union coach Urs Fischer - who had approached the Berlin ultras to ask them to remove the placards - said not only were the banners inappropriate, but they interfered with his side's ability to get the job done.
"I understand you want to show your opinion, but it should be with decency and respect. I didn't see that in these banners."
"It was very uncomfortable for my boys - such an interruption can completely steer a game in the wrong direction. In my view, these posters were completely unnecessary."