Leipzig, runners-up last season, are already 13 points off leaders Bayern Munich following their fifth league defeat of the campaign.
It was Leverkusen's second straight win and they moved back into third place on 24 points.
Leverkusen, who have yet to lose on the road this season, had an early effort by Moussa Diaby ruled offside but went in front when Floria Wirtz powered into the box to latch on to a perfectly-timed Exequiel Palacios pass to chip the ball over the keeper.
They added another goal in the 34th with Diaby rifling in from a cross by Jonathan Tah.
Leipzig, 5-0 winners over Brugge in the Champions League on Wednesday, were missing half a dozen players through injury and were toothless in attack until Andre Silva's powerful header in the 62nd cut the deficit.
The hosts' frustrating afternoon was complete when Dominik Szoboszlai's 88th minute penalty hit the post.