Zucker's shot trickled under the outstretched left leg pad of Sergei Bobrovsky, who made 26 saves. Minnesota goalie Josh Harding denied all three Columbus attempts in the shootout and finished the game with 20 saves.
"We scored a power-play goal, but I still thought our power play was bad," Blue Jackets coach Todd Richards said. "First period, it lacked intensity, soft plays, not shooting the puck, not winning battles. We had two power-play opportunities, and we end up the period with three shots. Disappointing, because it's been a focus."
Wild defenseman Keith Ballard skated onto a loose puck in the high slot and snapped a shot past Bobrovsky to tie it 11:36 into the third.
After the game, Minnesota coach Mike Yeo said his roster will be trimmed Tuesday.
"We're going to get down tomorrow," Yeo said. "Not our final number, but close to it. We want to make sure we get as close as possible. But we will have a couple more decisions to make."
Material from wire services was used in this report.