Croatian Mandzukic rose high to meet a deep Diego cross and head in the deserved equaliser in the 85th minute with the 2009 champions down to 10 men and having missed a bagful of chances.
Alexander Meier had put the visitors into the lead on the hour against the run of play, after Halil Altintop's shot was cleared, giving new coach Christoph Daum reason to smile.
Wolfsburg, who won the 2009 Bundesliga title under Felix Magath before his return late last month, had failed to find the net despite dominating most of the game.
Forward Patrick Helmes, who alone missed half a dozen chances, also failed twice to beat goalkeeper Ralf Faehrmann in one-on-one situations early in the second half before Meier struck on the break.
Wolfsburg, down to 10 from the 72nd minute after Germany international Arne Friedrich was sent off for a second booking, kept fighting and grabbed the valuable point that lifted them to 16th place on 28 points.
"We conceded a goal from an offside position and the red card was too strict," said Magath. "So given these wrong decisions I am happy that we still managed to get a point."
Cologne saw their chances of staying up also improve considerably when Milivoje Novakovic scored a stoppage-time goal to give them a crucial 1-0 win over Nuremberg and dent their opponents' European aspirations.
Slovenian Novakovic struck with the last kick off the game, tapping in a Slawomir Peszko low cross in the final minute of stoppage time to lift Cologne to 10th place on 35 points with Nuremberg stuck in sixth on 42, three off the last Europa League spot with six games left.
"It was a tight battle and in the end we managed to get in the lucky punch," said Cologne coach Frank Schaefer. "It was an important step that allows us to keep our target (of staying up) in sight."
On Saturday, Borussia Dortmund came from a goal down to demolish Hanover 96 4-1 to protect their seven-point lead at the top as second-placed Bayer Leverkusen stayed in the hunt with a 1-0 win at Kaiserslautern to move up to 58 points.
Champions Bayern Munich moved up to third place following their 1-0 win over bottom side Borussia Moenchengladbach on Saturday.
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