Sidney Sam scored the only goal of the game after 74 minutes to secure a hard-fought victory though Srdjan Lakic could have denied them when he hit the post late on.
Bayer find themselves on their own in third as Dortmund's victory over Hannover means they have a seven-point gap either side of them.
Lautern had the first chance of the match when Sam was adjudged to have fouled Adam Hlousek just outside the box.
Adam Hlousek took the free-kick from the left corner of the penalty area, sending it to the far post where Mathias Abel headed over.
Lakic then drilled an effort over from 22 yards as the hosts pressed.
Bayer were struggling to break down the home defence, and when Michael Ballack did get a shot in his effort was blocked by Christian Tiffert.
Leverkusen did finally have a great chance just before the break when Michal Kadlec advanced down the left and sent the ball into the centre towards the waiting Ballack and Simon Rolfes but the former Chelsea midfielder headed straight into the hands of Kevin Trapp.
Chances were thin on the ground in the second half so it was somewhat out of the blue when the visitors scored 16 minutes from time.
Trapp tried to clear Eren Derdiyok's ball into the centre, but only found Sam, whose left-footed volley gave the goalkeeper no chance.
Lautern's best chance for an equaliser came four minutes from time when Lakic headed Tiffert's corner against the post from five yards.