Nino Niederreiter scored into an empty net at 15:57 to make it 6-2.
Jarvis scored at 17:55 for the 7-2 final, tipping Cole's point shot.
St. Louis outshot Carolina 15-5 in the third.
"Third period, I thought we were the better team," Blues coach Craig Berube said. "We pulled the goalie early and they scored two empty-net goals and that was the end of it. But the way we played the third is the way we have to play hockey in my opinion. We were way more aggressive, on our toes, heavier to play against, heavier sticks, direct, north. Just had the will.
"I didn't think our start was that bad to be honest with you, but we did fall behind. First period was OK. Second period, we get scored on there pretty quick. I thought that had a real impact on our team that period."
NOTES: Svechnikov scored 24 goals in 68 games in 2019-20. ... The Hurricanes scored seven goals for the third time this season. ... Carolina center Jordan Staal won 15 of 21 face-offs (71 percent). ... Blues forward David Perron's eight-game point streak ended (14 points; 10 goals, four assists). ... St. Louis forward Vladimir Tarasenko was minus-4. Faulk and forwards Thomas, Buchnevich and Brandon Saad each was minus-3.