The home side could have taken the lead with just 14 minutes on the clock when the ball dropped to Ragnar Ache inside the area, but the in-form striker completely miscued his effort as a big chance went begging.
Ache was involved again just four minutes later when he was picked out from the left, yet this time he was unlucky as his header from point-blank range was well saved by Kamil Grabara.
All of the early pressure was coming from the hosts, and their third opportunity of note saw Marius Bulter’s cross find Kristoffer Lund, but the left-back’s header went just wide of the left post.
Shortly after, though, the home side hit the front in slightly fortuitous circumstances as Linton Maina made space for a left-footed shot from just outside the box, which took a slight but telling deflection off Moritz Jenz to wrongfoot Grabara and find the net.
Keen to respond, the visitors could have drawn level eight minutes before half-time when a ball over the top freed Patrick Wimmer, whose near-post effort was blazed over the crossbar.
Wolfsburg knew their second-half performance needed to be much improved if they were going to take anything from the contest, with their wait to register a first shot on target being an ongoing concern.
They really ought to have at least tested Marvin Schwabe just before the hour mark when Dzenan Pejcinovic was found in the box, but his strike rolled agonisingly wide of the right post.
With just over 20 minutes remaining and the game yet to be decided, Maina had a chance to net his second goal, only for his attempt from the right side of the area go narrowly off-target.
Die Wolfe were much-improved in the second half, although their lack of composure in the attacking third ultimately proved their undoing as they failed to create any further opportunities, slipping to a defeat that sees them remain 12th and just four points above the relegation play-off spot.
This morale-boosting and much-needed win for Die Geissbocke - just the second in their last 11 league matches - moves them eight points clear of danger, with a first clean sheet in 14 Bundesliga outings.
Flashscore Man of the Match: Kristoffer Lund (FC Koln)
