Die Wolfe took an early lead through a Bas Dost strike before Sidney Sam struck for the visitors to level the scores on the stroke of half-time.
However, second-half goals from Luiz Gustavo and Ricardo Rodriguez respectively were enough to secure a 3-1 win for Dieter Hecking's team and condemn Leverkusen to a fourth straight loss in all competitions.
Speaking after the game, Kiessling admitted that the two strikes after the interval were decisive blows and left Bayer struggling to take anything from the match.
"The goals scored by Luiz Gustavo and Ricardo Rodriguez were the deciding moments of this game," the 30-year-old German told reporters.
"We always tried to get to the ball first, which we did well at times, but falling behind cost us dearly."
The defeat is a serious dent in Leverkusen's Champions League ambitions as they look to secure qualification for next season's competition after a 4-0 reversal at the hands of Paris Saint-Germain in their last-16 first leg tie last Tuesday.
Wolfsburg's fourth consecutive win in all competitions took them to fifth place in the Bundesliga, just four points behind second-placed Bayer, but goal-scorer Gustavo refused to get carried away over his side's long-term aims.
"We're only concentrating on our targets and our style of play," the Brazilian midfielder said.
"It's working really well right now. At the end of the day our aim is still to achieve something of note this season."