Croatian striker Mario Mandzukic struck twice in the first half and substitute Ashkan Dejagah hammered in two more in the second after Cologne's Sebastein Freis had capitalised on a mistake by keeper Diego Benaglio to cut the deficit.
Magath returned to Wolfsburg last month after leading them to the 2009 Bundesliga title and his team are now in 16th place - the relegation playoff position - two points behind Eintracht Frankfurt.
"I hope this result will give us some sense of security for the remaining games," Magath told reporters.
"We had the right attitude, we fought from the start and that is why we won", he said, after club bosses read the riot act to his players in midweek, saying there was not enough commitment to fight against relegation.
In the only other match of the day, Nuremberg and Mainz 05 shared the points in a goalless draw, with Mainz holding on to fifth place that leads to the Europa League next season.
Bundesliga leaders Borussia Dortmund were forced to put title celebrations on hold on Saturday after a surprise 1-0 defeat at relegation-threatened Borussia Moenchengladbach cut their lead to five points.
Dortmund are on 69 points with second-placed Bayer Leverkusen, who beat Hoffenheim 2-1, on 64 with three matches remaining.
Champions Bayern Munich dropped to fourth place following their 1-1 draw at Eintracht Frankfurt with Hanover 96 a point ahead in third place as the two teams battle for third and the last hope of a Champions League spot.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
