In a rollercoaster game, Bayern found themselves 2-0 down at half-time before scoring two goals in two minutes to level and then taking an 83rd-minute lead through Leroy Sane. Leipzig, however, struck deep in stoppage time to equalise through Yussuf Poulsen.
The result put Bayern on 76 points, nine ahead of champions Leverkusen, who travel to Freiburg on Sunday. Bayern, with two games left and a much better goal difference than Leverkusen, will secure their 34th league crown should Leverkusen fail to win.
"In the first half we did not have the energy," Kompany told a press conference. "It was a good game for the fans and not a bad result for us, and I am very proud of the second half."
"The reason I am proud is we had quite a few players not there (through injury) and the image and energy was not too different than what we do in our best moments."
Bayern are missing several through injury, including Jamal Musiala, Dayot Upamecano, Alphonso Davies, Hiroki Ito among others.
Bundesliga top scorer Harry Kane was also missing on Saturday due to a suspension.
Kompany, in his first season in charge, is looking to bring the league trophy back to Munich after Leverkusen ended Bayern's 11-year league stranglehold last season with a domestic league and Cup double win.
Bayern can now secure the title in front of a home crowd next week against Borussia Monchengladbach.
"Congratulations to the boys and we are close now," said Kompany.