Svechnikov gave the Hurricanes a 1-0 lead 52 seconds into the game with a wrist shot through traffic from just outside the right circle.
Slavin made it 2-0 at 9:47 with a sharp-angled shot from the left side that beat Markstrom over his right shoulder. The play started when Slavin broke up a pass attempt with his stick and got the puck around Stefan Noesen.
"We had a little bit of O-zone time there and I knew they were tired, and they were just trying to get the puck out, and so just trying to have a good gap," Slavin said. "And ended up knocking it out of the air. I looked back and I think everyone on our team was changing, too, so just tried to throw it on the net and got lucky.”
Svechnikov scored 42 seconds into the second period, tipping in a shot from Seth Jarvis on the power play to extend the lead to 3-0.
"It's awesome," Slavin said about Svechnikov. "Obviously, he's a huge part of our team and can control the game out there with his skill, his presence, his physicality, his overall game, and when he's playing like that, it just makes us that much better of a team. It's huge for him, and hopefully he just keeps doing that."
Hischier brought the Devils to within 3-1 at 2:45, scoring off a rebound in front.
Meier then cut it to 3-2 at 7:34, getting to a loose puck and scoring off a spin from the right circle.
"The biggest thing was we got outcompeted the whole period, and that's not the way to start a period, and going down against these guys 3-0 is not in our plan," Hischier said. "So, we got to be way better than that.
"We haven't lost the series yet. We just got to go out there, win the road game and bring the series back here. That's all in my mind right now."
Burns scored at 14:14 of the third period to make it 4-2, and Svechnikov completed the hat trick with an empty-net goal at 16:43 for the 5-2 final.
"It's unbelievable. I mean, that guy so well-deserved," said Jackson Blake, who had an assist on two of Svechnikov's goals. "He's been bringing it every night in the playoffs, and it's been fun to see him, to play with him. I mean, on the empty-netter, I had to look for him. I mean, I'm happy he had that night, and it's good for his confidence. And I'm excited to see what he keeps on doing."