Leipzig, owned by energy drinks maker Red Bull, are three clear on 27 points following captain Willi Orban's 81st-minute winner.
Champions Bayern Munich, next best on 24, visit Borussia Dortmund on Saturday.
"We were always convinced about us and we never gave up," said Leipzig coach Ralph Hasenhuettl. "This was not an undeserved result.
"We had to pick the guys up at halftime. Then we showed amazing attitude in the second half."
Kevin Kampl gave Leverkusen a first-minute lead but Leipzig struck straight back when Julian Baumgartlinger turned a corner into his own goal three minutes later.
The fans had to wait until first-half stoppage time for another goal when Julian Brandt charged into the box to put Leverkusen back in front.
The hosts should have increased their lead when they were awarded a penalty in the 54th minute but Leipzig keeper Peter Gulacsi picked the right side and saved Hakan Calhanoglu's weak spot kick.
Leipzig, who watched about a dozen Leverkusen fans throw bags containing paint at their team bus on the way to the stadium, levelled when Emil Forsberg made a 60-metre sprint and his shot slipped through Germany keeper Bernd Leno's hands.
Orban then made sure of a memorable win, converting a header at the far post in the 81st minute as Leipzig claimed a sixth consecutive victory.
(Reporting by Karolos Grohmann; Editing by Ian Chadband)
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