
In a cagey first half, Christopher Nkunku’s stunning freekick gave the home side the lead in the 25th minute – the Frenchman’s 11th league goal of an impressive campaign.
Having broken the deadlock, Leipzig wrapped it up in the second half, with Dani Olmo arrowing home from outside the penalty area in the 54th minute and fullback Angelino adding a third following a swift counterattack three minutes later.
Leipzig had chances to add a fourth, with Nkunku denied by a fine save from Cologne goalkeeper Marvin Schwabe at his near post, but it was the visitors who completed the scoring after Tim Lemperle headed a stoppage-time consolation.
The victory saw Leipzig move into fourth on 34 points from 22 matches, above Cologne in seventh, with their rivals in action later in the weekend, as they continued their improvement under new coach Domenico Tedesco.