The striker's header that went through the side netting, a disallowed goal and a missed penalty resulted in a thoroughly frustrating night for Markus Gisdol's men.
Sidney Sam had put Sami Hyypia's side into a first-half lead at the Rhein-Neckar Arena before a Kiessling header ended up in the net via a hole in the side netting, but referee Felix Brych awarded the goal.
Hoffenheim's Kevin Volland had a goal controversially ruled out for offside with the game at 1-0, and Roberto Firmino missed a penalty in the closing stages of an action-packed match. Sven Schipplock pulled a goal back in the closing stages, but Leverkusen held out for the three points.
After a tentative opening, the match was sparked into life in the 26th minute when Sam cut in from the right and drove a left-footed shot into the corner beyond Koen Casteels.
Hoffenheim thought it had equalized when Anthony Modeste headed across goal and Volland applied the finish. However, the celebrations were curtailed with Modeste ruled offside, although replays suggested he was onside.
Leverkusen pushed to extend its lead but was largely frustrated by some dogged home defending, until a bizarre incident with 20 minutes remaining.
Kiessling rose highest to head Gonzalo Castro's header but put the ball just wide of the goal. But the ball crept through a gap in the netting, and the goal stood.
Hoffenheim was rightly aggrieved by the incident and pushed hard to find a way back into the game. It had the perfect opportunity to come back into the encounter when it was awarded a penalty in the 83rd minute. But Firmino's effort was saved by Bernd Leno before Modeste's rebound was deflected onto the post.
Hoffenheim did find a consolation with two minutes remaining thanks to Schipplock's effort, but could not force an equalizer.
The result means Leverkusen sits at the summit of the Bundesliga standings, with Bayern Munich and Borussia Dortmund due to play Saturday, while Hoffenheim remains 10th.