Mandzukic, Dejagah earn Wolfsburg win
Mandzukic put the 16th-placed Wolves in the ascendancy with goals after 14 and 39 minutes at the Volkswagen Arena. Sebastian Freis pulled one back for the visitors five minutes before the break, but substitute Dejagah netted twice in the second half to seal the three points.
After previously collecting just one win in their last 11 matches - and one in their last ten at home - today's triumph moved Wolfsburg two points behind Eintracht Frankfurt in the final position of safety.
"The relief is huge," admitted Wolfsburg coach Felix Magath, whose side face mid-table teams Werder Bremen, Kaiserslautern and Hoffenheim in the next three weeks. "I hope that this result gives us security for the remaining games. Today we have shown the right attitude from the beginning and have been rewarded with some success."
Cologne - now just three points and two places better off than their hosts - nearly went ahead after two minutes but Mato Jajalo's shot skimmed the outside of the post on its way wide. Wolfsburg thought they had taken the lead five minutes later only for Grafite to be ruled offside.
Magath's team did go ahead after 14 minutes, though. Sascha Riether fed Diego on the right wing and the Brazilian crossed into the middle, where Mandzukic slotted past Cologne goalkeeper Michael Rensing.
The Wolves doubled their advantage six minutes before the interval when Mandzukic headed home a cross from the left side from Marcel Schafer.
However, the two-goal cushion lasted only 111 seconds. Milivoje Novakovic supplied Freis and, although Wolfsburg goalkeeper Diego Benaglio got his hand to the shot, he could not prevent it from rolling in.
Rensing kept the visitors in the match with a superb save from Jan Polak's header two minutes into the second half. But the hosts moved 3-1 ahead after 58 minutes following a fine passing move. Diego had plenty of space to feed Grafite, who found Dejagah for a left-footed finish from 18 yards.
Cologne pushed forward looking to get back into the game but were caught on the counter attack as Wolfsburg rounded off their win in style, Dejagah slotting into the bottom-right corner from Mandzukic's right-wing pass.