Trocheck redirected Adam Fox's shot from the point on a power play for his 10th goal of the season to cut it to 3-2 at 13:58, and Kakko tied it 3-3 when he one-timed Artemi Panarin's feed at 14:05.
"It's huge," Fox said. "You could see the emotion from the guys on the ice, laughter and tripping over everyone in the pile. You don't see that all the time on just a goal, but when you're able to come back from 3-1 that quickly, the crowd gets really into it, and I think it's a big momentum swing. You get that jolt of energy."
Hughes was awarded a penalty shot at 12:50 of the second when he was taken down by Braden Schneider, but Shesterkin poked the puck off his stick.
"That's a key moment in the game," Devils defenseman Damon Severson said. "If we get a goal, we're up by a bunch. If they get a save there, they feel like they're still in the game. That's a 50-50 chance. Unfortunately, it didn't go our way, but we still had plenty of chances to win the game. We just couldn't get it done tonight."