Leipzig went into the clash at the Schwarzwald-Stadion three points clear at the top of the table and they made full use of the early opportunity to extend that advantage even further.
Naby Keita opened the scoring for the visitors after just two minutes before Timo Wermer’s brace and Marcel Sabitzer’s strike cemented a comfortable victory for the leaders.
Ralph Hasenhuttl’s men have now racked up seven straight league victories, moving them six points clear of Bayern Munich in second, and the records keep on tumbling.
The eastern German club are still unbeaten, have more points at this stage of a season than any other promoted side in German top-flight history and are on the longest current winning streak of any top-flight side.
Next up for Leipzig is a home clash against Schalke, who have struggled so far this season, on December 3 before an away trip to relegation-threatened Ingolstadt a week later.
A potentially crucial clash comes right before the winter break when the current leaders travel to defending champions Bayern on December 21.
Stoke could face a battle to keep Xherdan Shaqiri as reports have claimed Mark Hughes wants him at Southampton next season.
Bayern Munich have entered the race to Emre Can, who continues to talk up a move away from Liverpool this summer.