Leipzig got into the gear as the match progressed and restored parity also following a corner as Lukas Klostermann nodded home Christopher Nkunku's corner with 24 minutes into the first half.
Quick-fire goals from Vedad Ibisevic and Dodi Lukebakio early in the second half, followed by more from Matheus Cunha and Dedryck Boyata gave Hertha their second win in two games under new coach Bruno Labbadia.
Hertha Berlin's Dedryck Boyata planted a kiss on teammate Marko Grujic during goal celebrations.
Hertha Berlin player Jordan Torunarigha was subjected to racist abuse during a German Cup game against Schalke.
Hertha Berlin completed the signing of Polish striker Krzysztof Piatek on Thursday.
Bayer Leverkusen edged past Bayern Munich in a thrilling 2-1 win on Saturday, while a 10-man Dortmund side held on to their lead against Hertha Berlin.
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