The Bundesliga new boys, now unbeaten after 11 games, have a three-point lead on Bayern Munich, who are at Borussia Dortmund on Saturday evening in the battle of Germany's top clubs -- dubbed "Der Klassiker".
Dortmund rout Wolfsburg to go top in Germany
Carlo Ancelotti's Bayern need to win at Dortmund to retain top spot on goal difference.
"From a psychological point of view we really did very well in the second-half when we were behind twice," said Leipzig coach Ralph Hasenhuettl.
After exchanging goals in the first four minutes -- Leverkusen's Kevin Kampl scoring after a minute before teammate Julian Baumgartlinger's own goal drew Leipzig level -- Leverkusen's German international winger Julian Brandt put the hosts ahead again just before half-time.
Bundesliga: Ingolstadt add to Dortmund woes
The turning point came when Brandt earned a penalty on 54 minutes only for Hakan Calhanoglu's shot to be cleared by Leipzig goalkeeper Peter Gulacsi.
Swedish international Emil Forsberg equalised for Leipzig following an impressive solo run on 67 minutes and defender Willi Orban headed in the winner on 81 minutes for the Bundesliga upstarts.
Leipzig earned their place in Germany's top flight with four promotions in seven years and have now set a Bundesliga record run for a newly promoted club by going 11 games unbeaten.
The club, sponsored by Austrian energy drink giants Red Bull, have 27 points from 11 games with champions Bayern Munich on 24 points.
But the newcomers have come under fire from rival fans who believe the club's sponsors have undermined the German idea of football not being an advertising product.
On Friday night the team bus was sprayed with paint on its way to the BayArena stadium.
Borussia Dortmund boss Hans-Joachim Watzke even weighed into the debate during the week.
"For the first time, we have a case where nothing, but absolutely nothing, has developed in an historic fashion. We play football to promote a canned drink!" said Watzke.
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