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Leipzig captain Marcel Sabitzer converted a penalty and Dani Olmo, who shone in the attacking midfield role, grabbed a first-half goal for the hosts.
The victory left Leipzig a point clear of defending champion Bayern ahead of the champion's game against Union Berlin.
The home win capped a good week for Leipzig, which knocked United out of Europe on Wednesday (AEDT) with a 3-2 victory to reach the Round of 16 of the UEFA Champions League.
Elsewhere, Arsenal loanee Matteo Guendouzi scored his first goal for Hertha Berlin in a 1-1 draw at Borussia Moenchengladbach.
Guendouzi scored just after the break when Gladbach's Denis Zakaria lost possession on the edge of his area.
Gladbach, which also reached the Round of 16 of the UEFA Champions League in midweek, fought its way back and equalised through Breel Embolo on 70 minutes.
Freiburg ended a nine-match winless run with a 2-0 win over Arminia Bielefeld.
Nils Petersen hit the woodwork twice before Vincenzo Grifo converted a late penalty.
