The Slovenian scored from close range in the second minute of injury time, deflecting Slawomir Peszko’s cross past goalkeeper Ralf Schaefer.
Cologne rises to 10th, while Nuremberg stayed sixth.
Driven by a dominant performance from midfielder Martin Lanig, Cologne should have scored in the 68th when Novakovic volleyed Lukas Podolski’s perfect cross over the crossbar.
Novakovic missed another great chance with five minutes remaining, beating the offside trap but denied by Schaefer’s outstretched leg.
In the late game, Mario Mandzukic scored to salvage a 1-1 draw for Wolfsburg at home to Eintracht Frankfurt.
Alexander Meier scored for Frankfurt in the 59th minute and looked to have given new coach Christoph Daum a winning start until Mandzukic rose high to head Diego’s long cross past goalkeeper Ralf Faehrmann in the 85th.
Wolfsburg climbs one place to the relegation playoff spot, and Frankfurt rise one to 13th, four points higher.
The home side - with Felix Magath in charge for his second game - created most of the chances: Diego going close with a free kick in the 14th, before Patrick Helmes had an effort headed off the line by Meier. Helmes then fired the rebound over.
Frankfurt should have scored in the 38th, but Meier’s cross was too high for Halil Altintop in front of an empty net.
Meier again cleared off the line after the break, blocking Arne Friedrich’s effort.
Helmes then missed two good chances in succession, drawing his shot to the left in the 50th and another to the right two minutes later, before Mario Mandzukic missed another opportunity.
Frankfurt took the lead against the run of play.
Altintop’s effort after a good run was saved by Diego Benaglio, with the rebound falling kindly for Meier to shoot low into the far corner.
Wolfsburg continued to create chances at will: Arne Friedrich shot over and substitute Ja-Cheol Koo’s effort landed on the roof of the net.
Friedrich was unlucky to be sent off for a second yellow card with 20 minutes remaining after a verbal dispute with Frankfurt’s Maik Franz.
Wolfsburg pressed for the winner after Mandzukic had equalized despite its numerical disadvantage. Diego’s free kick hit the roof of the net, and Marcel Schaefer forced Faehrmann to make another crucial block.
Earlier, Podolski had the first real chance against Nuremberg in the 21st. Miso Bracko delivered a dangerous cross, but the Germany striker was unable to direct his header under the bar.
Jens Hegeler should have scored for Nuremberg late in the half when shooting straight at Michael Rensing with only the goalkeeper to beat.
