Emil Forsberg and Timo Werner combined well with each other to score once each and snap Gladbach's three-game winning run.
The win lifted the promoted club to 45 points in second place, with Bayern, who drew 1-1 at Hertha Berlin on Saturday, on 50.
Leipzig prized open the Gladbach defence following a long passing move, Werner eventually feeding Forsberg and the Swede scoring with a clever low shot.
Forsberg returned the favour in the 55th to set up Werner after Gladbach's Thorgan Hazard had a penalty saved by Peter Gulacsi on the stroke of halftime.
Jannik Westergaard set up a nervous finale with a powerful header as Gladbach pulled a goal back but they could not avoid the first defeat for coach Dieter Hecking since he took over in December.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
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