Trailing 2-1 late in the game, the top-seeded Blackhawks forced an extra frame when Duncan Keith blasted home a shot from the left circle with 2:46 remaining in regulation.
But in the overtime Zucker got control of the puck to the left of the net and fired in a quick shot from a sharp angle that beat Chicago goalie Corey Crawford on the short side for the game-winner.
Pierre-Marc Bouchard and Zach Parise each scored for the eighth-seeded Wild, who desperately needed a victory after falling behind 2-0 in the conference quarterfinal round.
Josh Harding, starting a third straight game in place of the injured Niklas Backstrom, turned aside 25-of-27 shots.
Johnny Oduya scored and Crawford finished with 34 saves for Chicago, which will again try to put a stranglehold on the series in Tuesday’s Game 4.
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