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.
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.
Wisconsin business offering 'therapeutic cuddling' forced to close
Selena Gomez drops F-bomb, walks off stage during Jingle Ball performance