Christopher Nkunku had the first opening of the game in the starting minutes but his effort curled wide of the bar.
Leipzig found the net through Marcel Sabitzer soon after, but his goal was overturned because he scored from an offside position.
The home side continued to dominate proceedings with the likes of Angelino coming close as well.
However, they managed to break the deadlock five minutes into the second half when Christopher Nkunku had his effort blocked but then scored from the rebound with an unstoppable volley.
Leverkusen goalkeeper Lucas Hradecky produced a spectacular display to deny the home team a comfortable win here.
Second-half substitute Lucas Alario came agonisingly close to scoring an equaliser for Leverkusen but Leipzig managed to hold on for all three points in the end.
The home side had one final opportunity to double their advantage but they hit the bar with the last kick of the game via a free-kick from Marcel Sabitzer.
The win tonight leaves RB Leipzig in second place, seven points behind champions Bayern Munich.
Meanwhile, Leverkusen continue there disastrous run of form having lost five of their last seven games.
It will be interesting to see if they can turn their form around in the coming weeks and put together a winning run.