Perhaps still reeling from their midweek DFB-Pokal semi-final defeat to Bayern Munich, Leverkusen made a sloppy start and were fortunate not to have conceded on multiple occasions inside the opening 10 minutes.
Said El Mala and Jakub Kaminski both fired narrowly wide after catching Die Werkself in possession in their own half, before El Mala called Janis Blaswich into action with a curling effort that was destined for the far corner.
Cologne were then guilty of not being sharp enough at the back, with Eric Martel’s square pass cut out by Schick, but the Czech international saw his strike denied by the post.
Blaswich was soon busy again to deny both El Mala and Martel, before another slack backpass allowed El Mala to steal in and round Blaswich, but with the goal gaping, the Cologne frontman could only hit the post from an acute angle.
Those misses proved costly before the break when Martel was perhaps harshly punished for handball just inside the Cologne area, allowing Leverkusen to hit the front from the spot.
Schick assumed responsibility and beat Marvin Schwabe despite the home goalkeeper getting a hand to it, with that the striker’s sixth goal in eight games against Die Geißbocke.
It was a cruel blow for a Cologne side, who were on top for large portions of the first half, but wastefulness continued to undermine their efforts following the restart.
Another promising move saw Linton Maina release El Mala inside the area, but Blaswich again stood tall to deny the young German and started a counter that saw the visitors double their advantage.
Aleix Garcia released Nathan Tella down the left, and his delivery was stabbed home at the back post by Schick for his sixth goal in five Bundesliga appearances.
It looked a long way back from there for Cologne, but substitute Luca Waldschmidt went some way to easing their task when he slotted home to reduce the arrears after Leverkusen had failed to adequately deal with El Mala’s dribble.
With the atmosphere transformed inside the ground, the hosts ultimately failed to generate enough quality attacks to snatch a late equaliser, with Edmond Tapsoba making a late goalline clearance to preserve victory for Leverkusen, who are now unbeaten in five Bundesliga trips.
Cologne’s first loss under Rene Wagner may not prove too costly though, as they remain five points clear of the bottom three despite an eighth defeat in 11 league head-to-heads.