The visitors stormed in front in the seventh minute as Kevin Pezzoni's header off a corner kick beat goalkeeper Diego Benaglio, who went off injured shortly after the goal.
Wolfsburg fought back and equalized in the 22nd minute as Christian Gentner struck on a loose ball after a poor clearance by the Köln defense, but the visitors would restore the advantage 12 minutes into the second half.
Sebastian Freis got involved in a cluster in the penalty area, but he managed to put his foot on the loose ball to beat backup goalkeeper Andre Lenz.
The lead lasted just two minutes, though, as Ricardo Costa got a goal on a rebound after Faryd Mondragón vacated his goal for an attempted clearance.
Köln, however, were not to be denied as Adli Chihi struck the winner in the 74th minute after receiving Taner Yalcin's cross.
BERLIN (AFP) - Defending Bundesliga champions VfL Wolfsburg on Monday sacked coach Armin Veh in the wake of Sunday's 3-2 home defeat at the hands of strugglers Cologne after just seven months in charge.
The defeat was Wolfsburg's ninth consecutive game in all competitions without a win.
Veh took over last summer from current Schalke boss Felix Magath under whom Wolves won the title last season.
Having already been dumped out of the Champions League, Wolfsburg are 10th in the Bundesliga with just 24 points so far this season having conceded 38 goals, the second worst defensive record in the league.
"The relationship between Armin Veh and the team was good, but unfortunately, the results were missing," said club manager Dieter Hoeness.
"We no longer had the conviction that we could change the situation together with Veh in the foreseeable future.
"The record of nine games without a win and the high number of 38 goals against in the Bundesliga speaks for itself."
While a successor is found for Veh, Lorenz-Guenther Koestner, who trains Wolfsburg's second team, will take over as caretaker coach for Friday's Bundesliga game against Hamburg.
Former Real Madrid and Barcelona coach Bernd Schuster has already been linked to the vacant job, but ex-Hamburg boss Huub Stevens, who is coaching Red Bull Salzburg has alread told German website Sport1.de he is not interested.