In a game with a lack of clear cut chances, Kießling broke the hearts of the home fans late on by stealing the three points for the visitors after playing against 10 men for nearly the full match after Naldo was sent off for the hosts just four minutes into the game.
The result will be hard one to take for Markus Weinzierl's side but they must bounce back next weekend as they try to move up the table.
Naldo sent off within four minutes
It didn't take long for the game to burst into life as within four minutes of the game starting, the hosts went down to ten men.
A mistake in defence allowed Javier Hernandez in on goal and Naldo trying to run back with him, clipped his heel and sent the striker to the ground and straight away referee Deniz Aytekin showed the red card to the defender to leave the hosts with a mountain to climb.
All the red card did though was make it an even more intimidating atmosphere within the ground and this seemed to galvanise the home side as they were the ones that went close to opening the scoring despite having one less man.
Every tackle that one of the visiting players made after the early red card, the whole ground was wondering why the referee didn't produce any cards.
Hosts better team despite being down to ten men
Yevhen Konolplyanka went close on a couple of occasions on the break from the hosts while Thilo Kehrer headed a good cross over the bar when he should have done much better.
As for the visitors, it really was a poor half from them as despite having lots of possession they rarely threatened to score as the game became a very scrappy affair.
Overall though even though there wasn't any goals in the first half, it was a great game to watch with the home side given as good as they got despite having one man less.
It was much of the same at the start of the second half as the hosts were the ones that kept having the chances as Konolplyanka's end product kept letting him down.
As the half went on though the hosts started to tire more as they decided to try and sit back and earn a well-deserved point.
Hernandez had the visitors first real chance when he was given the ball in the box but his shot was well saved by Ralf Fährmann.
Kießling steals the points for the visitors
Just as it looked like the game was going to end goalless, Kießling headed home to give the visitors all three points.
The goal came from a free-kick which the hosts felt was very soft as Hakan Calhanoglu found the big striker in space in the six-yard box and he guided his header into the bottom corner of the net.
The hosts were unable to respond with such little time left as the visitors moved up to eighth place in the table with a vital win for their season.