Svechnikov made it 3-1 at 13:01 of the third period. He poked the puck away from Rangers defenseman Adam Fox in the neutral zone and scored through the five-hole on a breakaway.
Carolina allowed 17 shots on goal, its fewest in 12 playoff games this season. That total also tied New York's season low for shots, set in a 3-1 win at the New Jersey Devils on April 5.
"That's just the type of game we play," Trocheck said. "We play a hard-nosed game, we play smart and above them. That's how we played all the regular season. We kind of got away from that the first couple games of this series, but when we play that way and we play our game, I like our chances against anybody."
The Rangers outscored the Hurricanes 7-2 in Games 3 and 4 in New York after being outscored 4-1 in Games 1 and 2 here.
"We've got to win one game," Rangers forward Chris Kreider said. "That's our focus. It's a little cliché, but there are a lot of things we can take from that game and do a better job of. Learn from that and win one game. Win the first shift, win the first period and go from there."
NOTES: Zibanejad has a four-game point streak (three goals, one assist) and three-game goal streak. Three of his six goals in the playoffs have come on the power play. … Fox became the first Rangers defenseman with 10 playoff assists in a season since Ryan McDonagh (13) in 2014. … Panarin and Kreider each was held without a shot on goal. … In their seven home playoff games, the Hurricanes have outscored the Boston Bruins and Rangers 25-8. … Teravainen has 10 points (three goals, seven assists) during a seven-game home point streak. … Carolina forward Jordan Martinook had two hits in 7:54 of ice time after missing eight games with a lower-body injury.