The home side had taken the lead after 12 minutes when defender Kevin Danso headed in from a corner.
However, Leverkusen, who are still within striking distance of fourth place, were level just three minutes later when Kevin Volland slotted home after being played through by Charles Aranguiz.
The visitors had an effort from Lucas Alario ruled out by the Video Assistant Referee for offside in the build-up before the same player later hit the crossbar.
Peter Bosz's men were not to be denied, though, and they went ahead three minutes into the second half through Kai Havertz's deft finish.
Another Leverkusen effort was chalked off by a VAR review, before Jonathan Tah knocked home a rebound from a free-kick on the hour and Julian Brandt added a fourth in the 88th minute to seal a third successive win.
Leverkusen are in sixth place, two points behind Eintracht Frankfurt, but having played a match more, while Ausburg, in 14th, continue to look over their shoulder.