Leverkusen came into the encounter winless in their last three league encounters, the last of which was a 1-1 draw against Werder Bremen on home soil.
It was a lively start for Berlin, who had the game's first opening through Mark Friedrich's close-range header that shaved the upright.
Berlin coach Urs Fischer was forced to make a change at the midway point of the half as Cedric Teuchert replaced Sharaldo Becker, who was forced off after a collision with Leverkusen's Faycal Tapsoba.
The visitors ended the first half as the stronger side, with Nadiem Amiri and Kerem Demiraby going close to finding the back of the net in the final 10 minutes of the stanza.
The woodwork came to Leverkusen's rescue shortly after the break when Grischa Prömel collected a pass from Teuchert before unleashing a powerful strike that cracked the inside of the post.
With the visitors struggling to break the deadlock, Lucas Alario and Charles Aránguiz were introduced for the final 20 minutes before Marius Butler replaced Taiwo Awoniyi for the hosts.
However, it was left the first-half substitute, Teuchert, to net the winner for Berlin with a neat finish after spotting Leverkusen goalkeeper Lukáš Hrádecký out of position.