The result leaves the Werkself on 62 points in third place, now ten ahead of Schalke in fourth. The 96ers, already all but mathematically out of the running for a Europa League place, can now definitively start planning for a return to the top table-third next season.
The hosts hit the ground running, with Jens Hegeler - a substitute no less than 22 times this season - making the most of a rare starting appearance to fire them in front in the sixth minute following a searching run down the left from Andre Schürrle. There was no let-up from Bayer after that, with Hannover keeper Ron-Robert Zieler preventing Hegeler, Schürrle and Kießling all adding to that early advantage before the latter started and finished the move that took him out in front on his own at the top of the Bundesliga scoring chart, heading home Daniel Carvajal's cross for his 24th goal of the campaign.
That was that in terms of goals through to half time and though the visitors made a bright start to the second 45, it was Leverkusen who struck just shy of the hour to put the result to bed, Hegeler sweeping home Lars Bender's cross for his own second. After that, it was all over bar the shouting - and Sobiech's goal for the Hannover road home in the 71st minute.
Line-ups and statistics