Coyle made it 2-1 with an unassisted goal at 12:10 of the third period, six seconds after a Minnesota penalty kill ended. Coyle got an odd-man rush with Chris Stewart, who stepped out of the penalty box, and shot over Bobrovsky's glove.
"I tried to use my speed and get to the net," Coyle said. "I had more room than I thought I would."
Panarin tied the game 2-2 with 5:12 remaining in the third when he scored on the power play from the right circle. Wild coach Bruce Boudreau challenged for goaltender interference by Alex Wennberg on Dubnyk, but the goal was upheld after video review.
Savard gave Columbus a 1-0 lead 1:16 into the game. Panarin intercepted a pass by Minnesota's Ryan Suter behind the net and passed to defenseman Dean Kukan at the left point. Kukan passed across to Savard for a shot past Dubnyk.
It was Kukan's first NHL point in his 10th game.
The Blue Jackets thought they had taken a 2-0 lead at 12:19 of the first, but video review showed Savard kicked the puck into the net.
The Wild outshot the Blue Jackets 20-11 in the second period and tied it 1-1 when Zucker poked in the rebound of a Jonas Brodin shot for his 20th goal.
"We lost battles at the beginning of the second. We've got to win more battles," Columbus coach John Tortorella said. "Without [Bobrovsky], we have no chance if he doesn't play."
Zucker has five goals and two assists in a seven-game point streak.
"When we get four lines going like that, we can overwhelm teams and get them hemmed in and bring pucks to the net," Dubnyk said. "There's a couple of goals that easily could have gone in with a little luck, and [Bobrovsky] played well as usual."
Tyler Ennis came close to giving the Wild a 2-1 lead late in the second, but Bobrovsky got a piece of his shot from the right circle, and the puck crossed the goal line just after time expired.
"The first 10 minutes of the second period were a perfect road game, getting it deep, shooting at the net, going at the net, doing all the simple things," Boudreau said. "Even after they scored in the first period, we didn't give them much."